Charging and boot up problem. Battery or board at fault?

This A1278 fell from the sofa onto its charging port, with the charger plugged in. It stopped charging and eventually ran out of charge. In the fall, the charger became unusable so I tried another but the machine wouldn't charge.

I replaced the dc-in board and now it will start if I bypass the SMC (debug mode?) but not otherwise.

When it is up and running, the battery is not recognised - neither the OS nor Coconut Battery.

There is no light on the charger when it is plugged in (even while running).

With the charger attached but no battery, if I press the battery check button the green LEDs do the swishy thing to show they're working.

I tested the contacts of the Mac's battery charging connector and had 12v across the two at the extreme ends (which dropped to 0v when running).

The charger is a new Apple 60W.

Does this sound like a battery fault or am I looking at a new logic board?