A somewhat unstable system, bluescreens are random (more than 3 different stop codes is almost ALWAYS hardware).
System has a terribly hard time booting, bluescreens/lockups/dead on start.
Tends to "mostly" run once booted...
Sounds like power supply dude.
Since you're about to pull your hair out and start RMAing left and right, do this first (it will cost you less time and money than packing up and shipping something):
1. Goto radio shack, pickup a 20W, 10Ohm resistor (typically ceramic block kind). You should be able to get it for less than a buck. If you don't already have a multimeter, grab a cheapo one for 14.95 or whatever.
2. Completely disconnect your power supply from your motherboard, drives etc. Flip power supply switch off in back.
3. Use a paperclip to ground pin 14 (green) to any ground (black). This will allow your PSU to kick on without being connected to mobo/case.
4. Stick one end of the resistor plus your black multimeter lead into a ground (black wire)
5. Stick the other end of the resistor + the red lead into a power line (yellow/red). The multimeter and resistor should be in parallel (serial baaad).
6. Fire up the PSU and see what kind of voltage you are getting. You should be within +/1 10% for your 12v and 5v lines. Testing with no load will often give you perfect voltages. Placing a load (the resistor) is going to give you the true story.