New Alternator, not charging

I have a 1996 Lincoln Continental 4.6 V8, 134k miles on it. While driving, the A/C cut out, dash illumination flickers, etc. I limped home, found the battery dead, alternator not charging and ran the battery down. I have changed the alternator, still am having the same symptom. I hooked up jumper cables to get the car running, then used the Multi meter to check the output of the new alternator. I got a reading of only 12.4 with the jumper cables hooked up, when I unhooked the jumper cables, the reading gradually dropped lower and lower until the car would have eventually died had I kept the engine running, but instead I just turned it off. The battery is not old and tested out ok at the parts store, the previous alternator however did not. I dont understand what else I should be looking for. I cant think of any reason the system would not be charging.

Any ideas?