Q: I just bought an iPAQ 5455 and the battery seems to be dead! It fully charged it and it powers off immediately when it's not in the cradle.

A1: Make sure the battery is snapped right in. Then go Start > Settings > System tab > Power > Standby tab. Move the "Standby period" tab left and right a few times between 12 and 72. Leave it somewhere in the middle. This fixed it for me; it might fix it for you too.
A2: Try loading the ROM update.