The controller will work fine with just the PnC connected, it doesn't need a battery to work with the 360, it'll just cry low battery every now and then is all.
Make sure L4 is still on the board, a good shot will sometimes knock that thing off there and then you'll have a dead controller. If it's missing, just jumper wire it and you should be good to go.
If L4 is on the board, then look around the Left and Right Sticks on the top side of the board for corrosion. If something is spilled on the controller it runs down and corrodes up traces and parts and can kill, or even half kill it. The areas around T1 and T4 are usually the main suspects there.
I've also seen R41 go bad and cause a dead Matrix, as well as a bad Via that didn't let power thru from the batteries.
Barring any of those being the problem, break out the DMM and start doing some comparison checks on a working Martix, keep it around for parts, or just bin it.