Hello,
I would try first running a memory test on the computer to see if there is a problem with the RAM. Memtest 86+ is one program that can do this. (Faulty ram can cause lockups, freezing, bluescreens, and reboots) If it passes the tests, try disconnecting all peripherals except for the hard drive and one stick of ram and see if it works. If it does, remove that stick of ram and try another one. Change them out one at a time to see if the system will not work with one of the sticks. Another thing to check is to try the ram in different ram slots, in case one of those is bad. If you can boot the computer, you can try running a stress test on your processor as well to see if it is giving errors. You can use a program like Prime95 for this. You can also try resetting the BIOS to its defaults to see if anything has been changed that caused instability. Usually there is a setting in the BIOS to restore defaults. If the problem started recently, do you have a system restore point that you can try restoring from that is before when the problem began? I would also run a malware/virus scan if possible to be sure it is not caused by malware.