This sounds like bad memory to me. When the computer attempts to use a particular memory address and it's bad, the thing pukes. It seems random, but if you could see which addresses are being used, I'll bet it happens everytime an address (or more likely a range of addresses) is accessed by the memory controller.
My guess is you have a bad DIMM. Less likely is that something on the motherboard went kaput, but it happens. Microsoft provides a memory tester utility on their website. You can find the program installer and instructions on how to use it here:
Microsoft Online Crash Analysis
Try that first and see if you can pinpoint the problem. If not, you might have to take the machine to where you purchased it and convince them that there's a hardware problem.