It hasn't been mentioned, and I think it bears mentioning, that if you decide to swap the alternator yourself, disconnect the NEGATIVE battery post first.
The vehicle's chassis is negative ground, so if you disconnect the positive battery post first and the wrench touches sheetmetal... well, you can guess the rest, considering even a dead battery can push well over 200 amps through a wrench.
Also, the alternator has a large (usually red) wire going to it that is routed straight to the battery, so if you replace the alternator yourself do not attempt to work on it without first disconnecting the battery.
I don't mean to sound stearn here, but take it from a guy that replaced a dead battery on his 1968 Cougar and turned a Craftsman combination wrench cherry red in about 2 seconds by bridging poles!! (I was just glad there was no acid explosion!)
BTW, on the GM alternator there are two connections, the hot wire (+, to battery) and a plastic electrical plug. The plug controls the charging circuit and if it comes disconnected, reduces alternator output to zero. Negative contact is through the alternator body-bolted-to-engine-block, so also be sure the engine block is securely grounded. The alternator is most easily changed from beneath the vehicle... it's a dirty job but totally easy to DIY.
One more BTW, the charging circuit control is run by the ECM... if the wiring between the alternator and ECM is interrupted, you have no charging, but that's very rare.