Complicating the situation was that the back door into the garage has been locked for a long time, and I have no idea where the key is. (There's no door from the house into the garage; that's one of several oddities I've learned to live with.) That hadn't been a priority until this morning. On the occasion last year when tigger91872 came over to help when the garage door was stuck because the car's hatchback door had opened and was in the way, he had thought he might be able to pick the lock, but we didn't get that far because I was able to use the car remote to get it to shut the hatch.
Trying the keypad repeatedly didn't work. Waiting a while didn't work.
So, I went to the door, faced away, and kicked backwards. It worked! The doorjamb broke next to the lock, and I was able to get into the garage, open the car, and, to my relief, pushing the button on the remote opened the garage door. (It had also occurred to me there might be a circuit breaker that had tripped, preventing the keypad from working, but I guess not.) Can't recall which TV cop or firefighter I learned the correct technique from, but don't try kicking forwards to open a door. You're likely to do more damage to your ankle than to the door or lock.
Glad I didn't have to call a locksmith and pay a rush fee to get my car out of the garage this morning. The knob on that back door is now unlocked, and at some point I'll get the doorjamb fixed and get the lock rekeyed. I actually have a spare lockset that I got from someone at some point. That'll probably do the job. In the meantime, sorry, there's nothing exciting to break into my garage for!