You should consult with a copyright attorney. However, I suspect you do own the rights - and you would have whether they had paid you or not, so long as the transference of rights wasn't specified in your contract.
You did have a contract, right?
Next time, make a contract, even a simple one. And try to get paid in advance, at least in part. I despise it when artists are taken advantage of, and this startup certainly did that to you. BTW, even without a written contract, in the US, you can still sue them in Small Claims court, so long as you are within the local jurisdictional limit.