As JeffDaemon indicated it could be down to any combination of hardware failure. But this much we do know about your laptop:
1. It's fairly old by now (at some point, laptops will simply die),
2. The 1-year warranty has expired long ago (any repair is going to cost money),
3. Toshiba actually expects users to replace the battery 'after a period of time'.
Here's some detailed information about your Toshiba:
You can either pay for an official Toshiba diagnostics run, or crack the machine open and start replacing components yourself. Off the top of my head, it sounds like a broken AC connector port. You can get those on eBay.
Best of luck,