Stop working.

Write a clear letter saying that you're disappointed that they are not holding up what you thought was the agreement, especially since they obviously also thought it was the agreement because they had paid the first few invoices.

Issue a final invoice, and say that you look forward to receiving payment and having a discussion resulting in a signed agreement as to how to go forwards.

Be professional. No agreement is worth anything except to be a clear statement as to what's expected. The exception to that is if you are prepared to go legal, and that's an entirely different ball game.

Look at your possible outcomes, and consider what actions you must take to achieve the best possible, given that you cannot control what the client does.

Would you really go legal? Would it be worth it? Unless you are owed many thousands, it won't be. Getting a lawyer to write your letter is one way to increase the chances of getting paid, but up the stakes if they continue to refuse.

It's game theory - draw an explicit decision tree with probability estimates and expected payoffs. It's what I did when I participated in a semi-hostile management take-over.