Unfortunately, this is one of those cases wherein it might be better to let it go. After attorney's fees and subrogation, you'd be out more money that you'd collect. The insurance company won't let you be "unjustly enriched" by suing the complex and collecting, and also collecting a claim from them ... they'll want their money back.
Sounds like an awful situation. You can try to approach the landlord and see if they are willing to settle anything out of court. If you're really savvy, you can try to file a claim against them in small claims court based upon negligence, if you can prove it. You may be able to get a small payoff in order to help you get a new vehicle, since but for them putting the straw down, the drain would have worked properly and thus, your car would not have flooded. That's the only argument you have. Good luck.