Just another to take: Download ultimate boot cd (search for ubcd on google) - download the iso and use windows 7 to burn the image to a cd-r (right click the iso file, open with windows disc burning)(if no windows 7 is availabel you can use any program that can burn bootable images to a cd-r ex:nero, roxio, there are some freebies on the web that work fine as well). put that in the problematic PC and reboot it, setting the pc to boot from cd instead of the hard disk. it will boot into a menu that allows alot of things - you will want to do this process 3 times.
first time: check the hard drive for bad sectors
from the ubcd menu select hard drive, then diagnosis, then scroll down to "seatools for dos" (there are two of these, the higher version is easiest to use as it provides a graphic interface, the lower version is text mode - either will work, your choice). You want to make sure the drive with windows installed is selected (if only one hard drive don't worry as its selected by default). then from the menu in the top of the screen choose to run a LONG TEST (don't bother with the short test, we are specifically looking for long test here). after this starts let it run all the way through - this will take a long time to finish. If you see any errors reported or the test fails, you can stop here as the drive is bad and needs to be replaced - you could try to clone it using some of the cloning tools on the UBCD (reboot into it again, select hard drive, cloning) but this will probably fail if there are alot of sector errors, you will most likely need to replace the hard drive and reinstall windows onto the new drive. If it passes, your hard drive is fine, move on to the second ubcd boot.
second time: check your memory for errors
from the ubcd menu select memory, then memtest86+. let this test run until it completes and reports 3 passes. If you have any errors in this test you will need to find the bad stick or sticks of ram (run memtest using indidual sticks and set the ones with errors aside). you should be able to pick up older ram fairly cheap on ebay or newegg - just hunt around. If there are no errors move on to the third ubcd boot.
Third time: check CPU/chipset
from the ubcd menu select CPU, then select one of the burn in tests. let it run until you feel comfortable all is well - these tests force the cpu to run intensive calculations constantly in an attempt to overheat it. if it overheats or has errors, you found your culprit - again you should be able to pick up a cpu cooler and cpu on ebay fairly cheap. if all is well, move on-
The last thing I would test would be your power supply (check this if any of the above are bad also - it may be the CAUSE of them going bad) - use a power supply tester to do this or try swapping the power supply with a known good power supply. If the issue goes away then If all is well, move on.
If all is well up to this point you definitely have a software issue. Not booting into safe mode means windows is pretty messed up. With windows XP you can boot from the windows xp install cd and when it boots up past everything it loads, there will be an listing for repair option under install windows. select this, it will boot up a dos prompt which wants you select the windows isntallation you want to work on - type the number next to it and hit enter. When it allows you to type again type "chkdsk /r" (without the quotes) and hit enter. This will take a while but let it finish - after its done see if you can boot into safe mode. if you can boot into safe mode with networking. download rkill.exe(google search it) malwarebytes from malwarebytes.org, but BEFORE you run either go to start > accessories > system tools > disk cleanup (this will take a while to load up). Check ALL the boxes in disk cleanup and hit ok (this will also take a while to finish). This deletes temp files etc viruses like to hide in. NOW run rkill.exe - this looks for and shuts down potential virus services a removal scan could keep you from removing if running. NOW install and run malwarebytes, performing a FULL scan. after you remove whatever it finds, allow it to reboot to finish removing. (VERY important to download these items before the disk cleanup, as browsing will create more temp files)
There is one last thing I would try before giving up on it if all this doesnt work to that point. There is a program called combofix
http://www.bleepingcomputer.com/download/combofix/dl/12/ which is basically automated windows repair on steriods. Run it, allow everything it initially asks you permission to do, and let it do its thing - it's saved me many times when nothing else in the world seemed to work.
All of the tools listed above are either open source (free to use) or free for home use.
removing viruses without software tools is pretty tedious. You can boot safe mode, go to start > run > msconfig.exe THEN select diagnostic startup. reboot your pc, running msconfig again, going through the services and startup tabs enabling one item at a time and rebooting, repeating this process until you have your issue again (then you know its caused by the last thing you enabled - googling this will probably give you details on which files etc you need to delete). If you choose to go this route you will need to spend some $ - for coffee.
Good Luck and let us know how it goes!