I'm gonna go with either heat or a failing/weak PSU.
When was the last time you took the side off of your computer case and blew it out with compressed air? If your answer is "huh", please click the following link:
http://lmgtfy.com/?q...+compressed+air
To aid you in this, i recommend HWmonitor, a free and easy to use temperature monitoring software.
If your temps are alright, you could have a weak/failing power supply. The only way I know how to test this without a volt meter is to actually swap power supplies and see if the problem goes away.
But just to explain:
When you first launch a game, it does more than just "load" the match. it's putting a LOAD on the CPU/GPU [with my UPS I can watch my wattage usage go from 160-220 up to 450-570 during the black screen] Either your CPU is choked with dust and it's causing the machine to shutdown to prevent damage, or the power is falling off causing the unit to die.
Good luck ^^