| Hi Mike,
Not sure about the connector from the alternator on the S. Two things to check though:
1. When you turn your ignition on is your alternator light coming on? If yes, then check 2 below. If no then you've got the same problem as me.
2. You may want to check three connections on the power steering pump (harder to do on the S given the larger drive shafts). Check the big power connector to the pump hasn't come loose (the most common problem, and has happened to me and a couple of other guys I know). Look for the thick red wire going to the pump and check the quick fit connector on the pump. Then check the smaller control wires (the two smaller wires going to the pump). And finally check the earth connection to the body of the car. Should be under the air cleaner / fuse box / ECU box in the S.
BTW on mine I've tried everything to get to the back of the alternator but no luck. Will be getting the manifold off tonight (all of 5 bolts so hopefully not too big a job) and see how I go. 
R56 MINI Cooper S JCW Challenge |