I have a PowerSpec B302 which was working until a few months ago and then it started locking up in the middle of the night (ironically when it wasn't being used). No BSOD, just lockup when it was resting (not standby or hibernation). The display would be blank. That went on for a couple of weeks until one day it wouldn't start up from a shutdown after one of the lockups. Since then when I apply power, it doesn't even get to the BIOS display but gives 3 short beeps.
From what I found this indicates a RAM problem. It had both slots occupied with 2GB sticks. I swapped them around, tried just one stick in each slot, and then tried RAM from another B302 I have (the one I'm using right now). The results were the same, no POST and 3 short beeps.
Further research seems to indicate this is a mobo problem. Does that sound right or could it be the cpu? Or even something else? The only other discrepancy I find is that the cpu fan hardly runs. So the cpu might have gotten hot, but I don't know how to tell just what the cause of the 3 beeps and no boot condition is.