It does use a different set of pins when it's charged in the car and when it's in the cradle. To answer your question - yes it can be fixed by replacing the connector. However, it could be the cradle. The cradle must be charging somewhat because it charged the backup battery.
Here's a link to PPC Tech that can do the repairs.
Pocket PC Techs - Accessories for AT&T 8925 WriteSHIELD® Combo DELUXE 2-Pak Kit
I believe they have repair facilities in GB. You'll just have to contact them to find out where they're located.
Good luck. :)