Laptop into wrong charger, how screwed am I?

First, what happened:

In a dark room, I went to plug my ASUS K55V in for a charge. As you may have guessed, I grabbed the wrong cable. What I ended up plugging in was...(prepare for cringe) the power supply for a Casio synthesizer. The instant it plugged in, the laptop shut down completely.

What happened next:

When I plugged the correct charger in, removed the battery, and placed it back in, the laptop actually started normally, and ran for about 20 minutes. It's worth noting that the battery was quite low before the incident, in fact, it probably had about 20 minutes left. However, after 20 minutes, the thing shut down. I can now start it for a few seconds and it seems like it's going to boot up normally, but it won't last longer than about 30 seconds, and often less than 10. Leaving the charge cable in for longer seems to slightly extend the time it stays on for.

I've heard about the nightmares people have experienced plugging the wrong laptop charger into their computer, and this wasn't even supposed to be a charger at all. On the other hand, the fact that I can start my laptop, and that it ran normally for awhile, makes me think that the battery may just not be holding a charge. What do you think, guys? Have I completely destroyed my laptop, or do I need to go battery shopping tomorrow?