Some things to look at:
Overheating problems- Use BIOS and your hardware monitoring software that should have come with your motherboard to check what kind of temperatures you are getting.
Power Supply (PSU) Problems- For a computer like yours, I would go with at least a 350W power supply. If you have anything less, it is very possible that your computer isnt getting enough power. Speaking of PSUs, you might also have a defective one. The easiest way to test for this is with a new/other PSU. Without another PSU at your disposal, then it pretty well has to come down to elimination of other potential problems to determine a insufficient PSU.
RAM- Faulty RAM will sometimes cause random errors/reboots. The best way to determine if RAM is your problem is to run your computer with one stick at a time, and see if the problem occurs for either stick. Also, running memtest86
will determine if you have faulty RAM.
Software- Viruses, Spyware, etc can cause problems that resemble that of hardware problems. Make sure you use a software or hardware firewall and an updated virus scanner and spyware scanner.
Hopefully that helps to lead you in the right direction