iPod Classic battery won't charge, inner rail is torn

I replaced the hard drive in my iPod Classic a couple of weeks ago. After I got it put back together it wouldn't charge up anymore, but would retain the charge it has when it's plugged in. Connects to the computer just fine.

To complicate matters, I took it apart again today, thinking maybe it was a loose battery cable. In the process, I tore one of the inner rails partially loose at one end. Is this repairable or do I need a new shell?

EDIT: As you can see in the first picture, the rail starts bending "up" after the outward bow and back "down" after the clip. Both solder points on either side of the clip are torn loose (second picture, the spudger is wedged between the rail and shell, it actually sits closer to the shell than depicted) and I'm not terribly confident in my soldering ability - most times I end up with about a pound of solder in a giant lump.

Also, any inputs on why the battery won't charge? Battery cable doesn't come loose under pressure and I don't think the receptacle on the logic board has come loose either. It does look like there may be a small "crack" in the ribbon, I can see a small amount of white in the bend.

Would this cause the cable not to work? Do I need a new one?