Suddenly my Toshiba Satellite A205 laptop died. No power.

First, check your power supply (the adapter). Is it putting out the required voltage to charge the battery?
If not, then you might have a dead battery and no way to charge it.
If the power supply is working and when you turn on the computer you get no lights, then you're probably looking at a new motherboard.
If you get startup lights and hear the fan, then it's getting power and you might have a video problem. But it sounds like, from what you wrote, there is no activity at all when you try to start it. That would be the power circuit on the motherboard, most likely.