That core specs of the PC are not that terrible, but the power supply does not look anywhere near a standard shape to easily replace. And you will need to track down a low-profle video card as well.
You can take out the components of the computer, and get a new case with a standard PSU, Antec is a good pick and even their lower end case/power supply combos will be way better than what you have now. Not much more work than replacing the power supply, and you get a regular case and can look for any size video card now.
I tried to find the full specs for the motherboard, aside from stating it's an nVidia chipset can't find the size. You do need to make sure that the motherboard meets ATX specs as far as the stand-off holes go, or...