I take it your car is an A3 of some sort.
The rear speakers are driven by the little amp in the sub, just to make it difficult to wire in an aftermarket decent HU. So changing the HU won't make any difference to driving the rear speakers, as the speaker loom at the HU only connects the front speakers and the Audi adapter plugs into the existing rear line out loom. The best, but not easiest, thing to do is run new speaker cable from the Alpine rear speaker outputs directly to the rear speakers. Unfortunately you need to remove the rear speaker panels to get to them (why they didn't use front loaders I'll never know). When you get to them, disconnect the existing speaker cable, you can leave them hanging as the Audi plugs are already insulated, or tape them to the bodywork to stop them rattling around. You normally run both rear speaker cables down the lefthand side, then take the right rear under the rear seats. This means you don't have the struggle of routing cable behind the steering column. Even if the rears were working I would still recommend you do this as the Audi rear amp is the size of a matchbox, and is driving that "oh so powerful" sub. You will still need to use the Audi adapter to get the line out to the sub.
You may find the multiconnector at the sub has another connector somewhere that feeds the rear speakers and has become disconnected. But I can't remember seeing one and if the sub is working, the amp and wiring that far must be ok as they all run off the same loom. I'm replacing the sub on my mates A3 Quattro this weekend with my special custom fit unit (see thread under A3/S3 section titled Bose sub upgrade), so I'll look out for the rear speaker connector, and post my findings.
