It's not a great idea to represent yourself in reinstatement traffic court. You do, however, have the constitutional right to do so. I would recommend spending an entire day in the reinstatement traffic court to observe how judges handle self-represented defendants to get an idea of how irritated they get at amateur lawyering. If you really want to represent yourself, you should purchase an hour of a reinstatement traffic attorney's time to have her or him coach you on how to handle things. A better choice is simply to hire an attorney.
While I do not handle parking violations there are services out there that do. The consequences are a money fine, which if paid late will have enhanced penalties.
It sounds like you have prof of payment, but it was not "properly" dsiplayed.