I'm having trouble with my computer (4-year old HP desktop running Vista) "hanging" shortly after startup. Not a BSoD, or the kind of crash you can ctrl-alt-del out of - it just freezes in place with no warning and stops responding to keyboard and mouse input.
I had this problem about a year ago, and after much googling it seemed like the most likely culprit was bad RAM. The built-in hardware diagnostics (PC Doctor or whatever it's called) never showed any errors, and neither did memtest86. The computer came with four 1GB sticks of RAM, so I wound up just taking them out one at a time - and eventually it kept on working, so I figured I did just have one bad stick of RAM and left it at that.
Here I am a year later and it's happening again - still no results from hardware diagnostics. The difference is that now it only seems to happen shortly after startup in the morning (whereas before it would randomly happen at any time)- after I've left the machine on for at least 5 minutes, it runs fine and won't crash for the rest of the day, until the next morning.
Because of the time scale involves, that makes me think the computer is literally "warming up" - although I've never heard of a computer crashing because it's too COLD...maybe some connection somewhere is a little off, the parts expand when they heat up and get in better contact? Stab in the dark but I don't have any other ideas.
Remove all but one stick of RAM. Does it boot up fine with just the one stick? If it doesn't, replace that one stick with another. Does it boot up fine? If not, continue doing it until you tried all the sticks of RAM.
If it still does it regardless of what stick of RAM is in it, I would say either the memory controller is fried, or it is a different piece of hardware. If it does it with only one of the sticks, then its that stick that is bad. Chances of all 3 (or 4, if you still have the one) sticks being bad is pretty low.
I would also find and download a hard drive diagnostics program that can test the integrity of the drive.