1990 Chevrolet S-10 Truck wont stay running

Was the truck doing the same thing before you replaced the alternator? It sounds like the alternator is wired incorrectly or is binding preventing the motor from running while it's plugged in. Basically the alternator is acting as though it's overloaded and is too hard to turn for the motor. You could take the belt off plug in the alternator and turn the key on it see if it's hard to turn by hand. Also and internally shorted alternator can act like a magnetic brake for the motor. A burned-out bearing will also do the same thing. And sometimes alternators are bad right out-of-the-box