Presumably the Toshiba will run off the power supply okay. So either the battery has failed or the power circuitry on the computer which charges the battery has failed.
I have this problem with a Dell, but fortunately I have an identical second model and can charge the battery on that.
Best bet is a Toshiba dealer or a friend with the same series of Toshiba -- ask them to see if your battery will charge on one of their machine and if it doesn't, you'll know you need a new battery.
Thanks I did find the problem, it was the AC adapter. With a volt meter I found out I was not getting the 19v that should be coming out of the AC adapter, I was getting zero.