A C182 SINGLE PLT MISHANDLED AND OR MISDIAGNOSED A CRITICAL ACFT PROB DURING TAXI. PRESSING ON TO HIS DEST; THE RPTR DISCOVERED PROP DAMAGE AFTER LNDG AT EYW.

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AFTER TAXIING APPROX +/-1 MI; ACFT WAS DIFFICULT TO MAINTAIN ON TXWY CTRLINE. I ATTRIBUTED THIS TO STRONG QUARTERING TAILWINDS AT FIRST. EVENTUALLY; CONDITION WORSENED TO EXTENT THAT IT WAS NEARLY IMPOSSIBLE TO FIGHT L TURNING TENDENCY OF ACFT. ADDITIONALLY; TAXI SPD WAS DECREASING. I PULLED ACFT OVER TO L SIDE OF TXWY TO TRY TO ASCERTAIN CAUSE OF PROB AFTER ADVISING GND CTL. IT SEEMED THAT THE L BRAKE WAS DRAGGING; MAKING ACFT PULL TO L. I TRIED PUMPING THE BRAKES ALTERNATELY TRYING TO FREE THE BRAKE. I ALSO WAS LOOKING AT L WHEEL PANT ASSEMBLY TO SEE IF I HAD ROLLED OVER ANYTHING; POSSIBLY LODGING IT BTWN TIRE AND WHEEL PANT. NOTHING WAS APPARENT. WHILE PUMPING THE BRAKES; I WAS INCREASING AND DECREASING PWR; IN AN ATTEMPT TO 'ROCK' THE AIRPLANE; HOPEFULLY TO FREE THE BRAKE. I WAS ALSO COMMUNICATING WITH GND CTL; UPDATING THEM OF MY SIT. I WENT THROUGH THE PREFLT CHKLIST AGAIN; AND CYCLED THE PARKING BRAKE. THAT SEEMED TO FREE THE OFFENDING BRAKE. I OBTAINED PERMISSION TO TAXI; AND WHILE TAXIING; APPLIED ALTERNATING BRAKES TO CHK THAT BRAKE WOULD NOT 'STICK' AGAIN. I MADE NORMAL RUN-UP AND ALL SYS; TEMPS; ETC; WERE NORMAL. CLRED ONTO ACTIVE; I APPLIED FULL PWR FOR TKOF. ACFT ACCELERATED NORMALLY; CLB WAS NORMAL AS WELL. UPON REACHING CRUISE ALT; CHKED THAT AIRSPD; TEMPS; RPM'S; ETC WERE NORMAL. UPON ARRIVING AT EYW; I TAXIED TO PARKING AREA WHEREUPON I SHUT DOWN ENG. LINE MAN PARKED ACFT; AFTER PLT AND PAX DISEMBARKED. I RETURNED TO THE ACFT AFTER IT WAS PARKED AND NOTICED DAMAGE TO BOTH PROP TIPS (LINE MAN HAD NOT NOTICED DAMAGE). THERE SEEMED TO BE AN EQUAL AMOUNT OF DAMAGE TO BOTH BLADES. THIS MAY ACCOUNT FOR THE LACK OF ANY APPARENT ENG VIBRATIONS. DAMAGE WAS LEADING EDGE GOUGES WITH VERY SLIGHT TWISTING AT BLADE TIPS. I DECIDED TO NOT FLY THE ACFT BACK TO OPF. I CONTACTED THE ACFT OWNER AND ADVISED THEM OF SIT. I DID NOT EXPERIENCE AN INFLT BIRD STRIKE; SO DAMAGE MUST HAVE OCCURRED WHILE ON GND. POSSIBLE; WHILE TRYING TO FREE L BRAKE; WITH ACFT ON L SIDE OF TXWY; AND WHILE THROTTLING UP AND DOWN; ACFT MAY HAVE CREPT CLOSE ENOUGH TO EDGE OF TXWY SO THAT PROP NICKED AN OBSTACLE ON TXWY EDGE. I DID NOT HEAR ADVERSE SOUNDS DURING THIS INCIDENT; THOUGH THERE WAS MUCH RADIO COM ONGOING AS WELL AS TYPICAL RADIO STATIC; ETC. ACFT PULLING TO L PROBABLY CAUSED BY PARKING BRAKE NOT FULLY RELEASED; AND/OR BRAKES NOT ADJUSTED PROPERLY OR STICKING L CALIPER.