The first thing I would try is scanning the computer for viruses, worms, rootkits, etc. If you find something here you should of course get rid of them as soon as possible. The next thing I would do is run a check disk, and the command in command prompt is chkdsk, if you find any errors here run the chkdsk /f to fix those errors. The next step would be to run a defrag to take care of fragmented files on the computer If there are any on the computer.
By following these instructions you should be able to bring your computer system back to life if not look to upgrade the hardware of the computer like the memory modules.