I think your problem lies with the PSU or the memory which your computer uses up while idling, because it is true that you can run WC3 easily with a 256 stick, but that's because the when the system is idling it doesn't take up as much cash. So, depending on what you mean by when you say, "My game randomly shuts down". Randomly as in, you can create your own game, stare at your screen with your base with those few peons and then it will crash all of a sudden? Or do you mean randomly as in you will play a little, and when you choose to go into a graphically intense map or terrain, you crash? If you crash even if you just stare at your base, I think it will be your PSU, but if it's because you go into a graphically challenging map, it will probably be your availble cash on your computer. Solution, try getting rid of the unwanted idling processes in the background, ie. Ad-ware, winamp/realplay/wmw process, etc. Or reformat so you start clean, or buy more ram. In my opinion, I would buy more ram, because if you would like to play even more graphically complex games like Half-Life 2, you would need 512 DDR for sure.
Luthien