Quote: "I was having similar symptoms with my RAM while playing intensive computer games."
That is a very good point. I had an issue on an old system where not only the RAM was dying (it was after a Linux crash of speculuar proportions) but also the BIOS was on it's last legs.
Not the bios itself but the flashram chip somehow had become damaged. This was back when they weren't welded to the mobo so was actually quite easy to fix mind.
If it is doing it on boot it could very well be the bios chip dying (about the only component you can't test unfortunately).
For the RAM, download a Linux distro, and run MEMTEST on boot (DSL is 50mb and has it so can be tested within an hour), if you run a standard test it'll tell you if the RAM is nackered; if you run an intensive test it'll tell you why it's nackered.
To test the CPU, run a CPU benchmark app; like specperf or cpumark.
To test the GPU, run a GPU benchmark app; like 3D Mark 05.
Make sure they are intensive. Also for Windows, right-click on My Computer and select properties. Choose the advanced settings and "error reporting". Make sure "reboot on crash" is unchecked. This will then flash up the bluescreen whenever the system calls a reboot. There is also an error.log (hidden system file) in the boot drive (on vista it is in a folder called boot) that logs all errors that have occured while windows has been running.
There is also an error log checker available in your administrator tools. You may also wish to check that.
If that isn't technical enough, then let me know; i'll get some caffiene and make a full post on how to do it under 2000/XP/Vista step-by-step.
One shame of Windows being so damn easy over *nix system is very few people know how to debug, error check, admin or lock down their systems at all let alone to a decent degree.
You'd be surprised at just how much you can gain from knowing Windows as well as most Linux users know their distro. Most of my comps tend to run far more stable, and quicker than others I know simply because I tend to optimise them once a month, and from installation tend to end up locked down from potencial attacks.
Too many security vunerabilities in the past that have come to bite me in the arse have taught me I needed to really know the OS inside and out.