Random Restart With ALL Browsers

I hope someone can help me. I have a computer (compaq presario 5300 US) with 512 mem and 1.1 ghz proc. The machine runs fine and will run for days unless I go to the internet with any web browser, IE 6-8beta, Opera, Firefox etc. Generally it will access the net ok, but when it encounters a page running any Java, it seems to accumulate errors then just goes black and restarts.No blue screen, no dumps, just black and a full restart. Sometimes it takes several minutes of running the program, such as a game called Brick Blaster found on the Zoomtown site. I have played this game for 5 minutes before the restart, or it can restart after the game first starts to load. I have found some Java errors using the OPera debug reporter but cannot make any sense out of them.I have installed a new Power Supply, changed out my ram strips, done a ram test, done a cpu stress test, scanned for viruses. Nothing found in any case. I am about to toss the machine in the trash, except it belongs to one of my best friends and for him, money is very tight.