I can see a couple of options but they depend on you being able to get to a command prompt with a working internet connection.

1. Install another desktop.


2. Burn a new USB installer from command line.

Install another desktop

This does not guarantee a working desktop though. Your problem might be something related to video card and also present in other desktops. Drop to a command line and start of with this:

sudo apt-get update

and then pick ONE of these (to install that specific desktop):

xubuntu-desktop 
lubuntu-desktop 
ubuntu-mate-desktop

I only listed a few (you could also install kUbuntu but for just getting a desktop to be able to make an installation disk might be overkill).

Burn a new USB installer from command line

Download Ubuntu from command line with

wget http://releases.ubuntu.com/14.04/ubuntu-14.04-desktop-amd64.iso

(change the url to a release you want. see http://releases.ubuntu.com and the directories below that for what you need). It will show something like this:

~/Downloads$ wget http://releases.ubuntu.com/14.04/ubuntu-14.04-desktop-amd64.iso
--2015-02-28 21:09:59-- http://releases.ubuntu.com/14.04/ubuntu-14.04-desktop-amd64.iso
Resolving releases.ubuntu.com (releases.ubuntu.com)... 
91.189.92.151, 2001:67c:1360:8c01::1e
Connecting to releases.ubuntu.com (releases.ubuntu.com)|
91.189.92.151|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 1010827264 (964M) [application/x-iso9660-image]
Saving to: ‘ubuntu-14.04-desktop-amd64.iso 6% 58,05M 1,36MB/s eta 7m 47s

and then "dd" the ISO to the USB flash drive. Pay extra attention to the device name. If you mess this up you could overwrite your current install... I tend to use dmesg:

[26005.823077] sd 7:0:0:0: Attached scsi generic sg3 type 0
[26006.953612] sd 7:0:0:0: [sdc] 30299520 512-byte logical blocks: (15.5 GB/14.4 GiB)
[26006.954291] sd 7:0:0:0: [sdc] Write Protect is off
[26006.954298] sd 7:0:0:0: [sdc] Mode Sense: 23 00 00 00
[26006.954912] sd 7:0:0:0: [sdc] No Caching mode page found
[26006.954918] sd 7:0:0:0: [sdc] Assuming drive cache: write through
[26006.972919] sdc: sdc1
[26006.976297] sd 7:0:0:0: [sdc] Attached SCSI removable disk

So that would be "sdc". This will burn it (skip the 1st one if you are still in Downloads, skip the 2nd one if it is already installed):

cd ~/Downloads
sudo apt-get install gddrescue
sudo ddrescue -d -D --force ubuntu-14.04-desktop-amd64.iso /dev/sdc

Results:

GNU ddrescue 1.19
Press Ctrl-C to interrupt
rescued: 63504 kB, errsize: 230 B, current rate: 196 kB/s
 ipos: 63504 kB, errors: 1, average rate: 12700 kB/s
 opos: 63504 kB, run time: 5 s, successful read: 0 s ago
Finished 

and an image of the freshly created USB ISO:

From Factory reset - Wikipedia:

Computer factory resets will restore the computer to the computer's original operating system and delete all of the user data stored on the computer.

This can be achieved either by re-installation of the OS or using a factory reset option. But in Linux, there is no option for factory reset inbuilt. So, it is required to look for alternatives which can achieve above said things.

While re-installation of the OS is the preferred method in order to remove users, user files and user applications but it is somewhat a tedious task. There is a tool called Resetter which would make "resetting Ubuntu" easier and will do what factory resets usually do.

Introduction:

Resetter is a tool which is used to reset Ubuntu installation to factory default. The Ubuntu system will go back to the state when it was installed for the first time. It finds all applications which are installed after Ubuntu fresh installation and delete them. Not just applications, it also deletes the users too. Deleting users means deleting their home too which means all user files and configurations. You don't have to install everything from the beginning. Just reset your Ubuntu to its factory defaults and start installing everything else.

Installation:

• 
  

  Download the latest release of Resetter and add-apt-key_versionX.deb from GitHub or use wget to direct download. At the time of posting this answer v3.0.0 was the latest release. To download using wget use:

  
  
  

  wget https://github.com/gaining/Resetter/releases/download/v3.0.0-stable/resetter_3.0.0-stable_all.deb
  wget https://github.com/gaining/Resetter/releases/download/v3.0.0-stable/add-apt-key_1.0-0.5_all.deb
  

  
  


• 
  

  Install some dependencies:

  
  
  

  sudo apt install libqt5clucene5 libqt5designer5 libqt5help5 python3-psutil python3-pyqt5 python3-pyqt5.qtsvg python3-sip
  

  
  


• 
  

  Install downloaded .deb packages:

  
  
  

  sudo dpkg -i package1.deb package2.deb
  

  
  

Using Resetter:

• 
  

  Open Resetter from Dash and authenticate. Authentication is required to perform administrative tasks.

  
  
  

  

  
  


• 
  

  To reset Ubuntu, click on Automatic Reset. But if you want to remove multiple packages at once click on custom reset.

  
  
  

  

  
  


• 
  

  Click "Yes" to confirm. You'll get a dialog which would list all the packages which would be removed.

  
  
  

  

  
  


• 
  

  Click "OK" to start. The factory reset will begin:

  
  
  

  

  
  


• 
  

  A new user will be created to access the system using administrative privileges. A dialog will appear which would show details about that newly created user. After that confirmation for Reboot will appear.

  
  
  

  

  
  
  

  

  
  


• 
  

  If your Ubuntu boots into TTY mode (command line/console mode), login with the credentials of new user and install desktop environment again.

  
  
  

  sudo apt install ubuntu-desktop
  

  
  


• 
  

  Welcome new user to the fresh Ubuntu. Use previously provided password to login.

  
  
  

  

  
  



• Modify Username and Password as per convenience.

Reinstalling can mean erasing everything, reformatting the partition, loosing all data and installing Ubuntu with a brand new /home/user directory. This is the common result when doing a google search.

This answer is about reinstalling Ubuntu and keeping /home/user directory. The following is from: Ubuntu Reinstallation

Ubuntu Reinstallation

Introduction

Sometimes reinstalling is the quickest way to solve a problem, for example if an upgrade failed or if your graphics driver is broken. When reinstalling, you're most likely want to preserve two things:

• 
  /home folder with your files and settings


• Entries in boot menu (if you have multiple OS installed)

How To Reinstall Ubuntu

Since Hardy it is possible to reinstall Ubuntu without losing the content of the /home folder (the folder that contains program settings, internet bookmarks, emails and all your documents, music, videos and other user files). This can be done even if /home is not on a separate partition (which is the case by default if you did not manually separate it when installing Ubuntu originally). This tutorial can also be used to upgrade Ubuntu (eg 11.04 -> 12.04 from a 12.04 live-CD).

Before doing anything

This operation should not damage your documents but, for security, backup your documents and settings (including /home hidden files) on external disk or DVDs. (eg via CloneZilla) Note: Some special applications settings may be in system folders, eg LAMP, see below in the thread.

Run the Ubuntu installer

• Run the UbuntuInstaller


• Follow the prompts until the "Installation type" (or "Allocate disk space") menu


• Choose the right option as described below:

Choose the right option

There are two possibilities - choose the one that fits what the installer is showing:

• If an "Upgrade 1X.XX to 1Y.YY" option is available (like in the screenshot below), choose it.

• Or, if the above option is not available, choose manual partitioning ("Something-else" option), then select Ubuntu system partition, set its mount point as "/". Be sure to keep the same format type, the same size, and untick the "Format" checkbox or all data on "/" will be deleted!. Also set other partitions (/boot, /home... see DiskSpace) if needed.

Then finish the installation process. (this may take several hours, like a normal install)

After reinstalling

After reinstalling, user accounts must be re-created with the same login and password.

See also

1. Discussion on the forum

Create a Live USB

• How to Create a Bootable Linux USB Flash Drive, the Easy Way

No standard factory reset for Ubuntu

• There is no standard explicit factory reset standard for Ubuntu, but there are several methods that can produce the same or similar results.

Your personal files

• Even if the current system does not work, you can probably copy or recover many or all of your personal files, when you boot from another drive, for example an Ubuntu live drive (USB pendrive or DVD disk).




• With a good backup routine you will have peace of mind, even if the drive crashes physically.




• Maybe your system drive or the file system(s) of your Ubuntu is damaged. You can check that and maybe repair the file system(s) according to this link.

Re-installation

• 
  

  A complete re-installation of Ubuntu is much faster than the corresponding installation of Windows. Re-install into

  
  
  
  • the same partition(s) as before or
  
  
  • different partition(s) or
  
  
  • the whole drive (if you no longer want to dual boot or multi boot).
  
  


• 
  

  A limited re-installation of Ubuntu can make things easier.

  
  
  
  • The most typical case is to preserve the /home directory, easiest using a separate 'home' partition.
  
  
  • Maybe you want to preserve some system files, that you think are good, from the /etc directory tree.
  
  



• There are already good and detailed answers here describing re-installation.

Fresh installation

• If there are problems, a fresh installation can be a good alternative to 'factory reset'.




• The [re-]installation can be to the original version and flavour of Ubuntu, but it can also be to new version or community flavour, a fresh installation. Please notice that you should stay with the same flavour of Ubuntu and use the same userIDs and names, if you want to keep /home.




• Compared to upgrading with do-release-upgrade it is often a reliable and efficient method to install a newer version, for example the most current 'first point release', 16.04.1 LTS, 18.04.1 LTS ... with long time support.




• But sometimes there are problems with hardware drivers, so you had better 'Try Ubuntu without installing', try live from a USB drive or DVD disk, before installing a newer version.

Resetter

• Using the tool 'Resetter' is described in an answer here.

Make an early backup. You may need it in the future

• 
  

  Think ahead and backup your Ubuntu system when it is new (or maybe the whole drive if a dual boot system). There are several backup tools. A full backup can be a cloned [compressed] image of the whole drive made with
  Clonezilla.

  
  
  

  When you want to reset your system, restore it using this backup.

  
  

Restore points or snapshots

• You can create several backups and use them as possible 'restore points' or 'snapshots' of the system, maybe once or twice per year.




• But you should also have a more frequent (daily or weekly) backup routine for your personal files, at least 'everything that you cannot afford to lose'.