How old was the battery before you bought it?
The only thing I can suggest is to attempt to charge it, discharge it completely (shouldn't take long), and try again.
Likely the battery has gone south. This will happen if you allow the battery to completely discharge (completely, when it can no longer support sleep mode) and is left for bit uncharged. That and heat are the only two ways to kill a clamshell battery. Even then, it's just outright kill the battery. This may not have happened.
Another option is some sort of surge that did some damage.
To state that the batteries don't have a memory, is correct, but only to an extent. The later iBooks and PBs have processors and a bit of flash ram onboard to prevent this kind of discharge, and to optimize battery life.