AN L1011 MADE 2 REJECTED TKOFS DUE TO AN ENG FUEL FILTER BYPASS WARNING LIGHT. ACFT INCURRED DAMAGE TO 7 MAIN TIRES.

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ON TKOF FROM TER; AFTER TKOF PWR WAS SET. CAPT SAW AN ENG VIBRATION/FILTER PRESSURE LIGHT ILLUMINATE ON THE FORWARD CAUTION AND WARNING PANEL HE RETARDED THE THROTTLES AND ABORTED THE TKOF USING REVERSE ON ALL 3 ENGS ABOUT 95 KIAS. I LOOKED BACK ON MY FE PANEL AND DID NOT SEE ANY ENG PROB. AS WE BACKTRACKED ON THE RWY; WE SPOOLED UP ALL 3 ENGS INDIVIDUALLY TO SEE IF WE COULD DETECT THE PROB. NO LUCK DOING THAT. THE BRAKE CHART SAID WE WERE IN THE READY AREA. SO WE DECIDED TO TRY ANOTHER TKOF. ON THE SECOND TKOF AT ABOUT 120 KIAS; THE #1 ENG FILTER PRESSURE LIGHT CAME ON ON THE FE PANEL AND WE ABORTED. THE BRAKE CHART SAID WE WERE IN THE NORMAL RANGE SO WE TAXIED CLR OF THE RWY AND WHEN WE GOT TO OUR PARKING AREA THE GEAR TRUCK LIGHT ILLUMINATED AND WE WERE INFORMED THAT 7 OF OUR 8 MAIN TIRES WERE STARTING TO DEFLATE AND SOME OF THE BRAKES WERE SMOKING. WE SUSPECT WE HAD A DRAGGING BRAKE PRIOR TO THE FIRST TAXI OUT BECAUSE THE CAPT COMMENTED AS TO WHAT HE THOUGHT WAS EXCESS PWR TO START ROLLING AND KEEP TAXIING.