The scheduled commuter flight was boarded with passengers and a crew consisting of 3 flight attendants, the first officer, and the captain for a flight to Pittsburg, PA. After a gate release, the aircraft was taxied to runway 29R and prepared for takeoff. The takeoff roll progressed normally until a point 4,200 feet from initiation. The crew reported a vibration and the left engine power diminished. The takeoff was aborted, but the aircraft speed at the time of the abort and runway distance remaining was insufficient to avoid departing the end of the runway. The aircraft became mired in the rain-soaked terrain up to the axle. Post-incident examination of the left main gear tires indicated a failure of the tire carcass. The tires had been retreaded 300 and 244 landings respectively prior to the failure. The carcass, however, had no records to show an operational or replacement history. The reason for the failure of the carcass was not determined. The cause of the initial power loss on the left engine was from ingestion of tire debris.