I've posted on here before about this but the advice I got didn't really work out for me so here it goes again. When I boot up my computer it frequently restarts and struggles to turn on, giving me boot options when it fails to start up. I get a serious error report that reports these:
C:\DOCUME~1\Family\LOCALS~1\Temp\WER7f76.dir00\Mini122908-06.dmp
C:\DOCUME~1\Family\LOCALS~1\Temp\WER7f76.dir00\sysdata.xml

but when I try to find them I can't locate them. (note I do have hidden files and folders turned on.)
Today I sprayed all the dust out of my desktop with compressed air (compy is a Compaq Presario SR1722X).

The main problem I am experiencing is that the computer will restart at random when I am on it. Mostly when I try and run Warcraft 3. I had a 1gb RAM card installed on it about 1 year ago and am running Windows XP service pack 2. I have done a factory restore and that didn't work either. I will run Hijackthis and post the log when needed.

If you have done a factory restore and the problem remains, what makes you think this is a malware problem?
There is every chance this is an hardware problem. Maybe your cpu heatsink needs reseating? Maybe your graphics card is getting too hot?
Considering it does it whilst you are gaming, these are the things I would be looking at, as well as the memory.

Thats what I was thinking when I blew the dust out this morning. Any good tips on how to check these things?

A software program would be the first thing I would get so that the temps can be checked.
ATItool should be able to check the graphics card temps.
CoreTemp should be able to tell you the cpu temps.

Both should be under load when checking for highest temp.

CoreTemp says "This is not an Intel "Core" Architecture based processor. This program will not continue." Even though I am running on a Intel Pentium 4 Inside.

I have ATItool running but I am baffled as to how to use it. If I hit load does that make sure the settings dont go above that?

For ATItool you just need to open the 3D window. That should start driving up the temp. You could also try using the 'scan for artifacts.'
Surprised that your PIV is not supported. Motherboard Monitor should work.
http://majorgeeks.com/download.php?det=311

Ok so I went to play WC3 again, and I had the ATItool minimized. I started to play and I could see it had maximized in the background and then the computer restarted. If it is a overheating graphics card, how do I go about fixing it?

Edit: I used ATItool to do a heatup and when it reached like 336.52 the computer turned off.

336.52 what?

336.52 on the core bar. it doesnt have units.

Sounds like you tried to find the maximum core speed instead of doing what I said and scan for artifacts?
Scan for artifacts then watch the temperature to see how high it goes. What graphics card do you have? Most cards should be good for 90C and higher, although lower is always better. My 9800GT with the stock cooler ran in the mid 80's before I put a 3rd party cooler on it. It now runs mid 50's.