Since the OP said "beep", I assume it's the normal single beep that says POST is clear. EDIT: Although running SpeedFan is a good idea (both for temperatures, processor frequencies, and for reading S.M.A.R.T). For some reason though, I've never managed to get it to work in Windows 7, even though it should.
In my experience, typical behaviour of a CPU overheat is first CPU throttling (things go slow but shouldn't stall) followed by an instant shutdown if it hits a certain temperature (set in BIOS). If the CPU is the cause of the crash, it's a sign of a badly processed instruction (Dark Star One described it as a math equation that didn't add up when checked, leading to system instability - i.e. crashing), which basically means the CPU is on its last legs (easy check - run a stress test for 5 minues).
RAM fault is the most likely cause of this particular type of crash, from my experience. Second most likely cause is the main HDD falling asleep or failing (so checking S.M.A.R.T is a good idea for checking the health of the HDD). Thirdly, it could be caused by bad system files (even a virus, but that's unlikely) being mishandled and/or causing a memory leak (the greater the memory leak, the more likely something's going to be mishandled... although usually the symptom is a great slowdown, but not a crash).
The two things that I can think of causing the DRRRRR sound, is either obstruction of a system fan (i.e. check the heatsink on the CPU to make sure all wires are clear - which could very well cause all the described symptoms) or feedback from the sound card/chip when crashing (symptom of a system overload).
The PSU is unlikely to be the cause of this crash unless it is being overdrawn (so knowing how many Watts the PSU supplies could help). CPU, I explained above. Motherboard, it's possible, but unlikely since it only crashes when browsing and gaming (both of which depend a lot on RAM and the primary HDD). Dust is also a possibility, making cooling far less effective and potentially creating static fields, but that's the easiest thing to check - a good old can of compressed air to clear out all the dust bunnies. EDIT2: Another possibility is the integrated graphics failing, but that usually results in BSoDs and failing graphics and it doesn't seem to be the case here since it seems to keep working even after the crash.
