Since you've already committed to not working with the company again, why not call the highest contact you have and, in as pleasant a manner as you can muster, politely request payment for services rendered? If it were me, it would go something like this:

"Hi ____, how are you?. I understand you've decided to implement the _______ project internally, based on the spec I wrote. I'm really glad it met your needs and I think it will be a great solution for you. I spent ___ hours working on it so I'd like to bill you $____ for my time. Does that sound fair to you?"

Then don't say anything else at all and just listen to his response. No justification or anything like that. He's either going to say yes or no.

If he says yes: "Great, I'll send the invoice over. Let me know if you need any clarification on the spec."

If he says no: "I'm sorry to hear that, good luck with your project and have a nice day." Then hang up and don't ever, ever take a call or answer an email from them again. Period.