You either have a bad battery or a bad contact to it. Power cable would not change.
I'd just get a new PDA or smartphone, Palm is pretty much dead as far as supported technology.
Where can I find a new PDA? I have looked on the Internet at different sources but only find used ones. I have a smartphone but still prefer my PDA for contact information. I also need to be able to download all the information I have in my PDA - either to my computer or to my smartphone (if no other option is available) or another PDA but I guess I can't do that if the battery is so low.
Thanks for any advice you can give.