I pulled the laptop apart and there was about a centimeter of highly packed dust in the heat sink. I've turned it back on and it's currently doing a virus scan happily enough now. No more problems so far.

My clue to the dust in the heat sink was that Toshiba is currently being sued for selling 5000-series laptops with a known heat problem. Apparently they have something in common: The filter is on the inside of the laptop.

I have an Toshiba Laptop as well 2004 i believe, and its started to do the same exact thing, It will stay on for alot longer then yours but it shuts off about 4 hours later once its turned on and i know that its because the laptop is overheating, you could try buying a can of compressed air to try and blow dust off from the fans in your laptop or you will have to try and get the fans inside of the computer replaced, I believe that i will have to get my fan replaced which could be costly.