The first and most obvious thing I would look for (so you doubtless already have!), is that the 'extra' locating tab on the back cover, designed specifically to hold the connector board there tightly onto the sprung pins (does yours have 6 or 8?) in the chassis, is not broken or damaged and is locating & locking-in correctly?
Also obvious.. but the Go will only charge on the TP Touchstone when 'Home Button' is lowermost & central.
Good luck checking out the electrical 'specs' ~ let us know how you go.
**Repair edit - 15 months later!
(Note to 'dkirker' @ #6 below ~ this works really well, so far!)
Unfortunately, I also snapped this extra locating tab completely OFF by mistake (they are not strong) and decided to try Sumi's 'workaround' repair.
Yes, peel off the relevant backing material AND the connector pads from inside the rear case and insert a small section of double-sided adhesive foam tape in the right position underneath all the connector pads before pressing it and the backing material back down onto the cover again.
This provides a nice raised & 'sprung' pad to continue to press the connectors successfully against the pins, conforms well to the curved shape of the back cover when refitted and actually seems easier than the alternatives, which were to try and 'superglue' the old snap-tab back into position, or solder longer wires in..