One possibility is that grease has gotten onto the brakes due to bad seals. We had that happen on a previous TT from the day we got it new and lasted a year until the dealer finally agreed to rebuild all 4 wheels. The symptom you describe sounds like what we experienced but there are other possibilities. I'd jack one wheel at a time and pull the break away pin and see if the brake is working. I'd pull each brake drum off to see what it looks like inside. Drums are easy to pull off.
As mentioned, wiring could be a possibility. Check the wiring in the A-frame area - the main positive wire from battery to mini circuit breaker(s) and to the splices inside the metal box. Check the battery ground connection to the frame. All connections and splices in this area are subject to corrosion as well as problems due to poor workmanship at the factory. I just rewired this wiring and found that the main positive wire from the batter was barely hanging on at the breaker and fell right out when I touched it. No power = no brakes = potentially dangerous.