800×600 is a rather low resolution for a modern computer.
There could be one of two things wrong: either your monitor is being wrongly detected, and X.Org thinks it can't handle a larger resolution, or the wrong driver is being used for your graphics card.
We are going to need some more information to figure this out.
There should be a file named /var/log/Xorg.0.log - this lists the settings of your monitor and graphics hardware (and some other devices) as determined by X.Org when you start up. Could you please copy and paste the contents of this file, as it can likely tell us what the problem is.
Also, to find out exactly what kind of graphics card you have, can you please run this, and post the output:
lspci | grep -i graphics
There is one quick thing you can try: I have an Intel graphics card and today received an update that claimed to fix a problem with detecting video modes on some cards, so it would seem worth updating your system and seeing if the problem goes away. To do that, you can run this command in a terminal (you may need to reboot after it's done):
sudo apt-get update && sudo apt-get dist-upgrade