Send a letter to the head of the board of engineers for that state. Send it certified, return receipt. In it state your attempts to become legally licensed to practice engineering in their state, including a chronology of your applications and follow-up. Point out that you are licensed in other states that have reciprocity or commity with their state. Tell them that their delays have cost you money in lost revenue and time spent trying to get them to review and act on your application.
Check the rules of the board in that state (they all have them). It usually states that when an application is received, they have a certain time period in which to act on the application. They've obviously failed to meet that. Point out that they have violated their own rules and that any further delay in acting upon your application will result in a complaint filed with the state's administrator (not sure what it is called in that state, but again...they all have one). Give them 30 days then file the complaint. If you get an adverse action on your application, then it's time to be an a$$. Go as high above their heads in the state as you can and make noise.