Alternator trouble

I just recently got a great deal on a 1988 IROC. The car was running off of the battery though, so put I a new alternator in it and it still has the same problem. What else can I check?
Also the key is stuck in the on position and the cooling fan runs all the time.

More concerned about the alternator situation though.

That must have been one hell of a deal.

Hilarious. I got it for the cost of the car transport rental. Lady just wanted it gone and didn't want the hastle of selling. Body and interior is in great shape. 5.7L 350... couldn't pass it up.

Fans on all the time is an indication that it is in limp home mode and could be something seriously wrong with the computer/system.