On November 27, 1998, at 1014 central standard time (cst), a Piper PA- 28-140, N10347, piloted by a student pilot, was substantially damaged when it over-ran the departure end of runway 12L (3,800' X 75', dry asphalt) at the St. Louis Downtown-Parks Airport, East St. Louis, Illinois, during a landing roll. Visual meteorological conditions prevailed at the time of the accident. The 14 CFR Part 91 instructional flight was not operating on a flight plan. The pilot reported no injuries. The flight departed East St. Louis, Illinois, at 1000 cst. The pilot said he landed the airplane on the runway next to Taxiway "H." He said he decided to fast taxi to the departure end taxiway instead of using a closer taxiway. As the airplane approached the runway end and associated taxiway he began braking. The pilot said he heard the right tire skidding and a short time later the airplane veered to the right. He said he released the brakes to regain control of the airplane. According to the pilot, the airplane ran off the end of the runway and collided with the Runway End Identifier Lighting system control box before he could regain control. According to the Federal Aviation Administration Prinicipal Maintenance Inspector conducting the on-scene investigation, N10347's brakes functioned according to the manufacturer's specifications. Examination of the tires revealed less than 1/32-inch of thread remaining. Skid marks associated with the airplane were not able to be identified on the runway.