Playstation PS Vita 1000 Phat Model , Not charging / Battery Won't hold charge, Can we fix it?

Picked this up from eBay for the sweet price of £45. Seller said it would power on for around 1 minute after a full evening of charge and then go off. Figured a simple battery swap would do the trick, and turns out I wasn't far off, came with a 16gb card aswell... bonus :)