I had the same problem with the pc im currently using to type this message, everytime i had to many applications open or i put my pc under "stress" it would shut down. I orginally thought that i did not have sufficent ram but i had 1gb and my pc was a reasonalbe spec so it should have handled what i was running fine but then one day it completely stopped working. It turned out the CPU was faulty and eventually died completely, i changed the CPU and havent had a problem since.
I am by no means an expert but i am just sharing what happend to me and how i solved the problem.
Many thanks Jack