Well, this certainly sounds like hardware is failure. To be sure your system is clean of malware, I recommend you run through
Cleaning Out Malware.
You also need to make sure your system is clean of dirt and dust too. You should open the case and inspect for dust build up. While in there, make sure all your fans spin freely and all connections are tight.
Inspect the motherboard for leaky capacitors. Leaky capacitors are a common cause of sudden system lock ups and reboots. Look for white to dark brown dried foam leaking from the tops or bottoms of the capacitors. The capacitors look like tall soda cans, many of which surround the CPU socket. Bulging capacitors are a sign leakage is about to occur. A motherboard with leaky capacitors can be repaired, but generally it is more cost effective to replace the motherboard.
RAM failure may also be causing this. To test your RAM, I recommend
MemTest86+. Select
Download - Pre-Compiled package for Floppy (DOS - Win). Unzip the file to a convenient location, insert a
formatted floppy disk in the floppy drive, double-click on
install.bat to install. Then, with the floppy in the drive, reboot the computer. The computer should boot to the floppy and start testing your RAM. Let it run for several passes or even overnight. You should have
no reported errors. Instructions to create a bootable CD version is available too. An excellent how-to guide is available
here.
