I'll outline the usual way to test this, but you ain't gonna like it (you're going to need lots of time)
First thing you want to do is remove as much 'fluff' as possible - by that I mean make the system as barebones as possible for it to boot up. One stick of RAM, no video card (if there's an integrated one), unplug all peripherals besides a basic keyboard/mouse, etc.
Then start Windows in safe mode or use some live-CD operating system such as Hiren Mini-XP or Bart-PE or Ultimate Boot CD for Windows. (You may have to create this on another PC).
Then you want to run some stress test software, such as Burn In Test, MemTest, Prime95. Go for the first one as it tests multiple components, and run the tests for a few hours at a time, so that a few passes complete. There's a decent chance that the tests will run successfully (which is kind-of what we want, otherwise diagnosis becomes harder).
You then want to shutdown and make a change to the system, maybe remove the 1 stick of RAM and insert another to test it, then run the tests again.
Then you might boot into normal Windows and try again. If there are faults here, try removing all device drivers in case one is buggy. Test again.
Then switch to using 2 slots of memory. Consult your mainboard manual to see which slots to use. Consult its website to see if your memory is on its compatibility list. I once had a similar issue and the fault turned out to be that my mainboard didn't like my Corsair DDR3 RAM. I tried DOA'ing many components but it wasn't until I switched to another brand of RAM that everything magically resolved. This is back when DDR3 was brand new and there weren't many options.
Add remaining RAM. Test again.
Add remaining internal hardware items one at a time, test again.
Connect external peripherals, test again.
Hope this helps.