Diagnosing and Solving the Problem
The first thing to do is ensure your problems aren't temperature related. Either using a desktop gadget or a hardware temperature monitoring tool, put your processor under loading using a program like OCCT or SuperPi and watch the temperature gauge. If it doesn’t elevate too much, and remains at at reasonable temperature, you can rule that out. If your computer crashes during the stress test, and temperatures are over 70 degrees Celsius, it's a reasonable conclusion that temperature is a factor. This means the cooling solution is either clogged up by dust or has failed. First try cleaning out your PC, and if that doesn't work, try installing a new cooler.
If temperature is not the issue, remove all hardware except the essentials, including a single stick of RAM, a single drive, and the graphics card. If your motherboard has on-board graphics, remove the graphics card and use that instead. Test the system again and try the activity that causes the crash. Work with a combination of drives, RAM and memory slots to see if you're able to find a system conflict that's causing the problem. This can be an ardourous process, but it's nessecary to pinpoint and solve the real problem.
If your computer does not boot at all, remove the processor and look for any signs that it may have suffered a hardware failure. This includes scorch marks, a smell of burnt electronics, or bent pins on the processor or the motherboard socket. Although it's rare for processors to be torched in this fashion, it's possible if your power supply or motherboard fails to properly regulate power - or if you crank the voltage way too high when overclocking.