My landlord does not have a required rental license and has violated the terms of my lease. Can I sue for back rent?

My city requires that a landlord hold a renter's license for every property that they rent as well as have an inspection done, both inside and out prior to the property being rented. My landlord does not have a license to rent and I have had multiple problems since I moved into my apartment. I have reported him to the authorities and I am planning on moving out. Is there anything that I can do to recover the money it's going to cost me to move again, as well as the back rent that I have already paid?