shapu's recommendations:
If you have not made any upgrades to the RAM recently, it is not that. Nor is it likely to be a hard drive problem.
First, check your CPU's temperature. First, install this program:
http://www.download.com/Core-Temp/3000- ... ?tag=mncolwhich monitors your CPU's temperature. Run the machine, and keep that program visible. See if it ever gets into dangerous temperature territory, and if it does, if that happens right before shutdown.
If it does:
Open the case, get yourself a can of compressed air from a computer shop and gently blow dust from inside the machine - don't hold the can in any position but upright, and don't spray continuously. Make sure you keep one hand on the metal chassis of the case at all times.
Now, with the case still open, turn on the machine, and make sure the fan on the CPU is running. It could be that the fan has died (they tend to go every couple of years), and replacing it is a very simple matter than anyone with 7 or 8 working fingers can do.
Or, it could be that too much dust has collected for the machine to work efficiently, in which case simply blasting it away will extend the lifespan of your machine. This can be easily determined by closing the cover up again, letting the computer run, and watching the temperature gauge.
If the temperature readings are NOT a problem:
Chances are that the video card is beginning to go. Have your dad (who built it, after all), tell you what kind of video card is currently in the machine - whether it's PCI, AGP, or PCI-E format. Go to Best Buy and determine what video card matches your needs and is in the appropriate format, and bring some suggestions back to your father (or just ask him to do it - again, he's the Dr. Frankenstein who built it, it's his monster).
Replace the video card. If you're not doing heavy gaming, concern yourself with price, rather than with any specific need. Radeons are fine for non-gamers. But of course make sure the chipset is compatible with any games you DO play - the Sims 2 and The Movies, for example, will not necessarily work on certain midrange graphics cards for no reason other than incompatibility, although the cards themselves could conceivably handle the load.