If it won't hold charge, and did with the old but worn battery, possibly something happened during the repair. Could be that the motherboard has been soiled or corroded. If so there is a chance that it can be cleaned (I managed when my iPod had similar symptoms).
You could go to the shop a tell them that the malfunction started after the repair, and would they accept responsibility. When they answer no, ask if they could - only from their wish to be helpful - give you a cleaning liquid plus instructions (there is repairmanuals on this forum if they prove to be completely uncooperative).
Several cleanings might be necessary. Focus on the area closest to the battery ribbon cable connector.
Good luck