After using Ubuntu to recover my documents, I began using it and transferring some of the files to a external hard drive.

I found the option "Screen Resolution" and I thought I might have a look. The resolution was set around (roughly estimated) 1100*800 (I'm not in Ubuntu, so it's around there), so I decided to change it to a higher resolution such as 1280x1024. The problem was the once I changed it, the screen flickered and a quarter (you can say the perimeter almost) of the desktop was static.

I've attempted to set it back to the original resolution, around 1100x800, except it made it worse. The desktop was not fullscreen as it was before and expect it "shrunk".

What I'm left with is a 720x480 (around there) resolution. I cannot click 'Apply' and I have to use Tab to move around the options. Switching desktops does not work either.

Can you get to a terminal?

If you type xrandr at the prompt, you will see a list of supported resolutions. You can then select these options either by index:
xrandr -s X (where X is the index in the list of available screen resolutions, 0 being the first in the list)
Or manually:
xrandr -s WIDTHxHEIGHT (where WIDTH and HEIGHT are your desired sizes).

Try something like 1280x800 for a starter and then see if you can work from there.

Hope that helps.