On February 15, 2001, about 1059 eastern standard time, a Piper PA-32-300, N15635, registered to an individual, had both main landing gear brakes catch fire during taxi, while on a 14 CFR Part 91 personal flight. Visual meteorological conditions prevailed at the time and no flight plan was filed. The airplane received substantial and the private-rated pilot was not injured. The flight was originating at the time of the accident. The pilot stated that after picking up the airplane from a maintenance company, he taxied to the runway with a passenger and took off. On takeoff, the left wheel brake grabbed a little and then let go almost immediately. He flew locally and returned to the airport, where he dropped off his passenger. He again taxied to the runway to fly to Vero Beach, Florida. During taxi, he felt the left brake grab again. He taxied to the end of the runway and when the left brake again grabbed, he elected to return to the maintenance company. The brakes failed and he began using the "emergency brake." As he approached the ramp at the maintenance company, he smelled smoke. He shut down the airplane's engine and heard a tire blow out. He got out of the airplane, at which time the second tire blew out. He saw both landing gear brakes on fire. Personnel from the maintenance company came to the airplane with fire extinguishers and put out the brake fires. The mechanic from the maintenance company stated he had performed a oil change and checked the condition of the brakes and battery. When the pilot taxied back to the ramp, he observed that both main tires were on fire. He got a fire bottle and put out the fires. When he opened the cabin door after the fires were out, he noticed the parking brake was pulled on to about 3/4. After the accident, while repairing the airplane for the pilot, he disassembled the left and right brake assemblies under the supervision of a Lakeland Police Department Aviation Officer. They found no discrepancies that would have caused the brakes to drag or lock prior to the accident.