My daughter had something similar happen when she tried to turn on her PSP after a few months of non use. Apparently, since the battery was without charge for an extended period of time the battery died and would no longer charge. Of course this happened a few weeks after the warranty expired.
Lesson learned? Now, I make sure to check on my trusty kindle keyboard every week or so to check on the battery status. So, far I found it on a critical battery screen a few times and make sure to charge it right away. Before, I would power off my kindle keyboard entirely however now I keep it on. It may seem counterintiutive, however the best way to extend a device's battery life may be to keep it on vs turning it off entirely. Reason being? It's easier to forget to check on a device's battery status with it off, risk the battery draining entirely for an extended period of time resulting in a bricked device.