Turns out the battery was indeed bad. Took it to Les Schwab for their free battery test and their little computer said it was "bad". The guy didn't give any detailed explanation of what exactly was wrong with it, just "sometimes it happens". Anyway, they gave me a new one under warranty, in and out in 25 minutes.
I'll monitor the engine starting response for a while but it seems that all's well that ends well, plus I learned a couple of new things about car batteries from this thread so thanks for everybody's contributions.
Still have your alternator checked. If the battery went bad it was for a reason. A bad alternator can kill a battery.
