Is my battery dead?

I have a Thinkpad T61 and this morning, without having touched the Laptop, the computer dies when I unplug it (it wasn’t like this yesterday). The battery says: “Computer is running on AC power. Laptop battery fully charged (66.5%)” and seems stuck there. It says the same even if I remove the battery. I’m running Ubuntu 9.04 (64bit).

Does anyone know if this might be something other than the battery? If not the battery, what could it be?