You're really lucky the battery didn't blow. Unfortunately I've seen this mistake several times before and the outcome can be as cheap as a blown fuse (rare) or as costly as a blown ECU. First check out your fuses, especially the one for your ignition/starter, if that looks good then I would replace that battery. Between the complete drain and the reversed polarity and the fact that it's over 3 years old anyway you will want a fresh battery anyway. If it's still dead then you more than likely fried the ECU. Unfortunately, more often than not I've seen this mistake call for a new battery new ECU(s) and fried wiring. Good luck... Let us know the outcome.