Hired to create a logo but not paid, do i still own the rights

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.

In the US? Go to small claims court to get your money.

If they are using the logo (signs, letterhead, web site) then you need a cease and desist ruling from a judge.

Never give a client the final version of a design until its paid for. Pur a proof mark on all rendering you do for proposals.

All this stuff. Also, half at concept and half for final product with code to remove watermark

Yeah, it gets complicated in that it could be perceived as a work for hire. Either way, though, of course -
* a contract is necessary, spelling out rights and the payment plan
* a third to a half payment up front
* specs and samples only get sent with watermarks
* final payment and then the code to remove the watermarks is provided