A Boeing 737-4Q8, N405KW, was substantially damaged while attempting to push back from a gate at the Miami International Airport, Florida. An employee of the company that provides ground support stated that the towbar was first connected to the airplane. He then positioned the paymover and attempted without assistance to connect the towbar to the paymover. The paymover then moved uncommanded rearward and collided with a container loader. The engine of the paymover was then shut down and the captain and a ground support supervisor who were on the flight deck inspected the airplane for damage; none was noted. The captain returned to the flight deck and the supervisor boarded the paymover. The supervisor stated that while standing on the paymover he disengaged the parking brake, applied the normal brakes, and started the engine of the paymover. Immediately after the engine was started the paymover moved uncommanded forward and attempts to stop the paymover using the normal brakes were unsuccessful. The paymover then collided with the towbar and a ground power unit which was pushed into the fuselage. The supervisor further stated that he operates similar paymovers daily. Following the accident, damage to the tug was repaired; however, the normal brake system of the tug was not worked on. The neutral safety switch which is designed to prevent starting of the engine with the transmission in drive or reverse was operationally checked for failure or malfunction, with no defects noted. Additionally, postaccident operational testing of the normal brakes at near full acceleration revealed no evidence of failure or malfunction. According to the cargo manager, the paymover involved in the accident had been in the shop for maintenance on August 28, 1995, and during testing, the engine started once while the transmission selector was in the “drive” position. Attempts to duplicate were unsuccessful. The paymover was returned to service. According to the training manager he experienced a similar occurrence involving uncommanded movement of the same paymover but the normal brakes stopped the paymover. He also stated that discrepancies with ground support equipment are verbally reported to maintenance. PROBABLE CAUSE: “Improper planning/decision by the company driver of the vehicle (paymover) and uncommanded movement of the paymover for undetermined reasons. “