Just in case anyone still needs to figure this out - I used the W-D-40 and it worked! I squirted some in, jiggled the keyboard around a little, and then I noticed that the W-D was seeping out the other end of the keyboard (where the power button is - not where you put in the batteries). So I jiggled it a little more, hit the sides of the tube where the batteries go, and after a couple of minutes the bad battery slid out. It was only very slightly corroded - normally I wouldn't even notice that tiny amount of corrosion - suggesting to me that the battery tube area (sorry don't know the technical term) is very tight. Probably as soon as you get the message that the batteries in the keyboard are about to run out, you should change the batteries. I always wait for them to actually die which probably had something to do with it.
Anyway - glad I solved this problem for myself and I hope I can help someone else with this technique!