[Spridgets] Dead battery and alternator?

[ryan.kubanoff at comcast.net]

I left my lights on when I went to work this morning and needed a jump to get started inorder to get home.  I drove 35 minutes home on and off of highways at 3500-4000rpm.  I stopped to get a haircut andd then couldn't get the car started again without another jump.  I have no idea how old the battery is (from previous owner) but shouldn't the alternator have recharged the battery enough to start the car in that time?

So i am planning on replacing the battery at pep boys tomorrow but what about the alternator?
Thanks
Ryan