splice
The new changer is most likely not compatable with the old cable. Best case scenario, a shop can splice the new cable into the old cable if they really know what they are doing. Your best bet is to just replace your stock head unit with an Alpine unit. You can find a half decent one for less than $150 anywhere on the Web. You need to chase down that new cable because you need it for the installation.
Suggestion #2:
Call Alpine technical support. Give them the model numbers of both changers and ask them if they are interchangeable. My guess of course, is that they are not.
Suggestion #3:
Some of the older changer cables have a ground wire that is screwed to the car's chassis right before the cable connects to the changer. It is possible that the ground wire was pulled loose when the changer was stolen and the stereo shop neglected to re-ground it when they completed the installtion. (If they used the old cable.) The ground wire is designed to isolate the harness from bleeding--induction of foreign signals from one wire to another. This could make your sound crappy and would be the quickest, easiest fix possible. However, I think this is a remote possibility