Ah, the business workhorse 6310i...how I loved mine! Unlikely to be a battery problem, it is huge, the whole back of the phone, and holds its charge for ever. Are you using the original charger? It is sensitive that way, and the input jack size is critical. Sadly, I just sent all my chargers for recycling, having amassed about 20 over a few years...always the way, keep 'em for ages, bin 'em, someone wants one...
However, I do have the phone! If it's of any use, let me know and I'll pop it in a jiffy bag. You can give your favourite charity a wee donation to cover postage.