Shows Li-On battery charged when plugged into AC, shuts down when unplugged

Here is a palm article on the battery not holding charge-

http://kb.palm.com/SRVS/CGI-BIN/WEBCGI.EXE/,/
?St=42,E=0000000000826384196,K=1280,Sxi=19,Case=Obj(30029)

My battery loses its charge very quickly
Like all Lithium Ion batteries, the battery in your device will eventually wear out. If you charge your device fully but it loses power after a few hours (or sooner), it may be time to replace the internal battery.

Sounds like you already did this. Do you have someone you know who has the same battery you could try? Or try your battery in their device?


Also this site looks good -
http://www.ipaqrepair.co.uk/ipaq_battery.php

Step #11

You can connect it via USB and let it charge that way a little while, then try charging it normally. It's called trickle charging-

Trickle charging
Some Palm devices have the ability to "trickle charge" from a USB port on a PC or Mac. This means that it receives a very small amount of charging from the USB port, even if it is not connected to its AC charger. If your device is capable of this function, the charging time will be significantly longer for a trickle charge (depending on the power rating of the PC USB port). However, the device may not charge at all on an unpowered USB hub (or for example off off a keyboard).