IPAQ trouble - won't turn on

I have an HP IPAQ 310 that I run X-C Soar on, that won't turn on. :-(

I left it in my bag for a few months and didn't use it, and wouldn't be surprised if the battery ran down.
Before that period, it worked fine and was not in a condition to suffer physical damage.
When I plug it in, the amber charge light illuminates, but even overnight charging never shows the battery fully charged.
The unit won't turn on at all, whether plugged in or not.

Searched HP forums and didn't find this exact issue with this model

Does anybody know if this is how it will behave when the battery finally gives up the ghost? I'd hate to spring $25 or more bucks on a battery for a dead unit.

Bill Palmer
wfpalmer at gmail dot com