A B737 FLT CREW ABORTS A TKOF DUE TO A MALFUNCTION IN THE SPD BRAKE SYS. THE PROB APPEARS AGAIN IN THE LNDG AND THEN IS WRITTEN UP BY THE FLT CREW.

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LANDED EARLY ON THE 1ST LEG OF THE TRIP; I NBOUND FROM MCO; HAD 50 MINS ON THE GND. WE RAN THE BEFORE TKOF CHKLIST ABOUT 10 MINS BEFORE THE PUSH; THE BEST I RECALL. ALL CHKLISTS WERE ACCOMPLISHED AT A NORMAL PACE AND WITH MINIMAL DISTRS. UPON TAKING THE RWY FOR THE CHANGE OF ACFT CTL AND AN FO TKOF; THE THRUST LEVERS WERE RAISED AND AS THE ENGS STARTED TO CATCH UP; I ADVANCED THE THRUST LEVERS SLIGHTLY WHEN THE TKOF WARNING HORN SOUNDED. AS WE ACCOMPLISHED A LOW SPD ABORT; I NOTED THE FLAPS AND SPD BRAKE IN WHAT APPEARED TO BE THE PROPER POS. AFTER CLRING THE RWY THE CAPT RESEATED THE SPD BRAKE LEVER AND CHKED THE THRUST LEVERS FOR A HORN AND GOT A GOOD CHK. WE RE-ACCOMPLISHED THE CHKLIST AND DEPARTED. ON SHORT FINAL WITH ATC SPD CTLS DELAYING THE CONFIGN; WE DID NOT GET AN ARM LIGHT ON THE SPD BRAKE LEVER. CAPT DIRECTED TO CONTINUE AND AFTER CLRING THE RWY; A CHK OF THE CIRCUIT BREAKERS REVEALED A POPPED WARNING SYS BREAKER. WE ADVISED MAINT TO MEET US AND BRIEFED THEM AND THE NEW CREW ON THE EVENTS. TO THE BEST OF MY KNOWLEDGE THE CAPT DID A THRUST LEVER CHK AS WE ROUNDED THE CORNER; FROM THE GATE; TO TAXI W IN FRONT OF THE TERMINAL. RECOGNIZING NO-ONE'S MEMORY IS 100%; I DO BELIEVE IT IS A GOOD POSSIBILITY THE WARNING SYS WAS HAVING A LITTLE MEMORY/SYS PROB ITSELF. SUPPLEMENTAL INFO FROM ACN 631185: PUSH AT ABQ GATE AND TAXIED OUT TO RWY 8. WHILE TAXIING AROUND THE TERMINAL; I ACCOMPLISHED THE THROTTLE BURST WITH NO WARNING HORN. UPON THE ARR INTO DEST; COULDN'T GET THE SPD BRAKE ARM LIGHT TO ILLUMINATE AND WE WERE IN A PHASE OF FLT THAT DID NOT ALLOW US TO TAKE TIME TO CHK THE CIRCUIT BREAKERS. FUTURE INCIDENTS MAY BE AVOIDED IF THE THROTTLE BURST IS INCORPORATED INTO THE 'BEFORE TKOF' CHKLIST AT THE 2000 FT REMAINING POINT OR AFTER BRAKE RELEASE WAITING AT #2 FOR TKOF AS PER THE FOM.