It could be any of those as well as the power supply.Does anyone know if this problem would be related the MOBO, RAM, or Processor?
If you have more than one stick of RAM in the machine then I'd try to run it with only one stick of RAM at a time and try each stick. It's highly unlikely to have more than one stick die at the same time so if it still fails with each stick of RAM individually then it's probably not the RAM. You could try to run MemTest86 to check your RAM. It doesn't require any operating system installed. From the sound of things MemTest86 will probably lock up but it's worth a try anyway.
I'd also make sure the CPU fan is turning because overheating can cause lockups and fans have been known to die. Mechanical things tend to be the problem more often than electronic components.
It's a bit of a hassle but you can test the power supply by borrowing one from another computer. I can't seem to download your motherboard manual but it looks like your BIOS can monitor the power supply voltages. You could try going into the BIOS to see if your voltages are in range. The important ones are 3.3 volts, 5 volts, and 12 volts. They're supposed to be plus or minus about 5%.
CPU and motherboard problems are hard to trace without swapping parts. Just from my own experience I'd say the CPU is the least likely to expire. One thing you can do with the motherboard is look for bad capacitors. They are responsible for lots of problems. This page shows you how to spot problems. Basically the tops of the capacitors bulge or they start leaking goo. The ones most likely to die are the ones near the CPU. They generate the voltage for the CPU and if they go the computer crashes and hangs.