Does My 12V Battery Need Replaced?

My 2007 Prius has about 76,000 miles on it.

It appears we left the dome light on for a week while visiting relatives, and now the thing is pretty dead.

We had a neighbor jump it and drove it around for about 20 minutes. I hoped this would let the alternator recharge the battery, but when I came home and parked it, the car didn't even have enough juice to lock the doors and it certainly won't start again without another jump.

Should I try driving it around some more to try to recharge the battery after another jump? It costs $180 to replace, so I'm not especially thrilled at the idea of swapping it out.

Also, this question may be silly, but I suppose it'w worth asking: what are the chances of the battery being replaced under an extended warranty?

 

Thanks. My wife is getting a new battery as we speak.