Any way around problem with battery/logic board?

I know Macs pretty well, but this problem has me stumped.

I'm pretty sure I've got a bit of a logic board problem on my MacBook Air, but I was wondering if there was any way I could--get around it.

Here's my issue--when my MacBook's battery is plugged into the logic board (internally), everything is slow. The mouse is slow, the whole computer is slow. It's hard to use. Doesn't matter if the MagSafe charger is plugged in or not. But if the battery is unplugged (and the MagSafe is plugged in, obviously), everything is fine.

Here's what I've done: SMC resets, NVRAM/PRAM resets, and it's DEFINITELY not the power settings within OS X (brand new install, also).

Is there any way around this issue? I really don't want to shell out for a whole new logic board.