The laptop failure symptoms:

The laptop will not turn on when I try to start it from the battery. When the laptop is turned off and plugged into the AC outlet the battery charge LED doesn’t light up. I know that the battery is not charged and the LED should light up when I plug the laptop into the AC outlet. The laptop starts fine when it is plugged. When I move the mouse over the Toshiba Power Icon in the lower right corner, the balloon will pop up and there is a line in there: Battery Remaining: N/A.

The problem repair procedure:

You can easily fix the problem just by updating the BIOS. Toshiba says that the BIOS version should be at least v1.30. So, go to Toshiba website and click on Downloads. Select your laptop model and find any downloads for the BIOS. In the BIOS change history you will see the description of changes.

After I updated the BIOS, the battery charging problem disappeared.