BSOD & Freezing (Win 7 64 Bit)

Hey folks.

I'm seeking some help with my Desktop PC, with the following specs;

Microsoft Windows 7 Enterprise Edition Service Pack 1, 64-bit
Intel(R) Core(TM) i3 CPU 540 @ 3.07GHz
3.1 GB RAM
ATI Radeon HD 5670

I'm quite the avid gamer, having been so for the past 3 years that I've had the PC. Sadly, over the past few weeks, I keep getting BSOD and a rather odd other 'freeze'. Typically, the BSOD can be quite random, but the other 'freeze' (which causes the screen to look like an old-TV after loosing signal) happens if I try to play a game instantly after the PC had booted.

It may also be worth noting that my screen sometimes will not connect, after a BSOD.

Just wondered if you guys had any idea as to a solution to this problem? I have an external HDD + two 500GB ones within the PC with plenty of free room - I am unsure if that helps deduce if it's a space-issue or not.

Thanks in advance to anyone who takes time out to read/help with this,
Adam.

EDIT: I will also add that if I leave the PC standing for about 15 minutes, it tends not to BSOD or freeze for as long as I use it after that period.