It sounds like a worn out charging port. You either have to replace the whole board or just replace the charge port on the board. The guide to remove the motherboard can be found here: Palm Treo 680 Motherboard Replacement.
While it's easier to replace the board, it's more expensive then it is to buy a whole new phone. I would suggest replacing the port on the phone, or retiring the phone and buying something newer or a phone like this used and using the old phone as a parts phone. This is because replacing the board is more expensive then a whole phone and you do not know if the IMEI/ESN on the new one will be active on another line, or usable at all for that matter. If you get a whole phone that's clean it's easier to check a whole phone instead of a bare motherboard. You need to verify the IMEI/ESN on the new board, if you can do this before you buy the board at all.
Yes, you can replace the board if you want but keep the risk of doing this in mind and weigh the risk with the cost of your board, and you can then decide if you want a whole new phone or just a board replacement.