MacBook Pro will *only* run with disconnected battery

Ok, so, my friend spilled a scotch and soda on his mid-2009 Macbook Pro, and I'm trying to suss out the extent of the damage.

The computer will boot and run normally off of AC power with the battery disconnected. With both the battery and AC adapter connected, however, the it will shut down halfway through the startup sequence (after the chime, but before the grey Apple logo.) Furthermore, if I reconnect the battery while the machine is up and running, it will shut off immediately.

(Also, the battery test button does nothing, no matter what is connected or not.)

So the question I'm left with is whether it's the logic board's battery-in port that's problem, or if it's just a bad battery. Obviously, the ideal next step would be to see if the machine starts up with a known-good battery in place, but I unfortunately do not have one to try it out with, and I'd rather not spend the money to buy one, only to find out that it's useless because the MBP's logic board is faulty.

What do you think the likelihood is that it's only a faulty battery causing the shut-downs? Is it worth risking the $150 to find out? Or is it pretty much certain that the logic board is bad?