ACFT COMMENCED TKOF ON WRONG RWY AT CLE. CAPT RECOGNIZED HDG DIFFERENCE EARLY IN TKOF ROLL AND ABORTED.

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TAXIED OUT FROM GATE. ACTIVE RWYS WERE RWYS 23L/R. AS I TAXIED ON TXWY LIMA CLE TWR CLRED ME FOR AN IMMEDIATE TKOF ON RWY 23L AS APCHED TXWY WHISKEY. TFC WAS ORIGINALLY LNDG ON RWY 23L WAS MOVED OVER TO RWY 23R. THE TAXI TO RWY 23L REQUIRES USING A PORTION OF RWY 28 TO LINE UP ON RWY 23L. AS I ENTERED RWY 28 I INADVERTENTLY BEGAN TO ADD PWR AND BEGAN A TKOF ROLL ON RWY 28 WITH TFC LNDG ON RWY 23R. THE AIRSPD DID NOT REGISTER ON THE INDICATOR BUT MOVEMENT BEGAN. I CLOSED THE THROTTLES AND WENT TO REVERSE WITH FULL BRAKES AND THE ACFT SLID ON THE PATCHY ICE AND SNOW. ACFT THEN STOPPED PRIOR TO RWY 23R BUT SLIGHTLY PAST THE POINT ON RWY 23L WHERE I COULD LINE UP FOR TKOF. I MADE A R 180 DEG TURN AND THEN LINED ON RWY 23L FOR TKOF. IT WAS FORTUNATE THAT WE STOPPED PRIOR TO RWY 23R. AT THE TIME I STOPPED THE TKOF (FO'S LEG) CLE TWR WAS CALLING FOR AN ABORT BUT HIS CALL WAS GARBLED BY THE XMISSION AT THE SAME TIME BY ANOTHER ACFT. THE JUNCTION AT TXWY JULIET FOR RWY 23L/R IS CONFUSING DURING DAYLIGHT HRS AND NOT LIT PROPERLY FOR GUIDANCE AT NIGHT. THERE WERE ICE AND SNOW PATCHES WITH SOME BLOWING SNOW. I HAD A FAIRLY NEW FO AND BRAND NEW SO THAT NIGHT. I HAVE BEEN TO CLE MANY TIMES AND HAVE ALWAYS FELT CLE NEEDED TO IMPROVE LIGHTING AND SIGNAGE AT THIS SAME AREA ON THE ARPT. AS WE TAXIED ON RWY 28 I ASKED THE FO IF THIS IS THE RIGHT SPOT AND HE REPLIED TO THE AFFIRMATIVE. THE FACT IS MY DIRECTIONAL GYRO SAID 280 DEGS WHEN IT SHOULD HAVE READ 237 DEGS AND I WAS BEGINNING A TKOF FROM AN INTXN ON A SHORT RWY AND THE WRONG ONE. FINALLY WHEN WE TOOK OFF; CLE TWR SAID 'IF IT'S ANY CONSOLATION; YOU'RE NOT THE FIRST THIS HAS HAPPENED TO BEFORE.' I CALLED CLE TWR ON ARR AND SPOKE TO A TWR CTLR AND HE SPOKE WITH THE SUPVR. THEY STATED THAT THEY WOULD NOT BE VIOLATING ME AND THAT THIS INCIDENT HAS OCCURRED NUMEROUS TIMES BEFORE AT THE SAME INTXN. I RUSHED INTO THE IMMEDIATE TKOF IN THIS CASE ON THE WRONG RWY IN A POORLY LIT AREA. I SHOULD HAVE PROCEEDED MORE CAUTIOUSLY OR STOPPED WHEN IT DIDN'T FEEL RIGHT. PERHAPS SOMETHING CAN BE IMPROVED ON HERE IN BETTER GUIDANCE IN CHARTS; LIGHTS; OR MARKINGS FOR THIS NOT TO OCCUR AGAIN. SUPPLEMENTAL INFO FROM ACN 323111: AS I LOOKED UP; WE WERE LINED UP WITH WHAT I THOUGHT WAS RWY 23L (IN FACT WE WERE LINED UP ON RWY 28). I BRIEFED A QUICK BEFORE TKOF CHK; 'FLAPS 5; FULL PWR; RWY HDG UP TO 5000 FT.' THE CAPT SAID SOMETHING LIKE 'YOUR THROTTLES.' I INITIALLY STOOD THE THROTTLES UP AND WAITED FOR THE BLEEDS TO CLOSE; THE ACFT BEGAN TO ROLL; I THEN ADVANCED THE THROTTLES TO FULL TKOF PWR. JUST AS THE ENGS WERE REACHING FULL TKOF PWR; THE CAPT PULLED THE THROTTLES TO IDLE; WHILE A SIMULTANEOUS GARBLED RADIO XMISSION WAS MADE. ALL I CAUGHT FROM THE RADIO WAS '_____________ RWY _____ ABORT.' IT ALL HAPPENED PRETTY QUICK AND I WASN'T SURE WHAT HAD HAPPENED UNTIL WE CAME TO A STOP. THE AIRSPD INDICATOR HAD NOT COME OFF THE PEG; AND I ESTIMATE WE WERE GOING 20-30 KTS. THERE WERE NO TFC CONFLICTS; AND WE STOPPED WELL SHORT OF RWY 23R. THE CAUSE OF THIS INCIDENT IS QUITE CLR; WE LINED UP ON THE WRONG RWY; AND I FAILED TO CONFIRM OUR HDG PRIOR TO TKOF. I MENTIONED EARLIER THAT MY HDG SET MARKER WAS IN FACT SET TO THE CORRECT HDG. I CAN'T SAY FOR SURE THAT I LOOKED AT IT PRIOR TO BEGINNING THE TKOF ROLL; IF I DID IT DID NOT REGISTER THAT IT WAS 50 DEGS L OF THE ACFT HDG. WHILE IT IS COMMON TO INITIALLY FLY THE RWY HDG; THERE ARE MANY DEPS THAT REQUIRE A TURN AFTER TKOF; THIS MAY HAVE CONTRIBUTED TO MY NOT CATCHING THE MISTAKE. CONTRIBUTING FACTORS: ONE OBVIOUS FACTOR WAS ALLOWING OURSELVES TO GET RUSHED; AND NOT STOPPING TO CLR UP THE CONFUSION REF OUR POS PRIOR TO TKOF. THE NIGHT LIGHTING CONDITIONS ALSO WERE A MAJOR FACTOR. I SAW JUST WHAT I EXPECTED WHEN I LOOKED UP TO TKOF; WHITE RWY LIGHTS ON BOTH SIDES OF THE RWY. THE RWY INTXN TKOF ALSO CONTRIBUTED TO THE ERROR. SUPPLEMENTAL INFO FROM ACN 322965: A COMMAND AND RESPONSE CHKLIST ITEM TO HELP CONFIRM RWY. AN EXAMPLE WOULD BE: COMMAND: 'RWY AND HSI'S' AND RESPONSE:'RWY 23L; HDG 230 DEGS.' THIS CHKLIST ITEM TO BE COMPLETED WHEN ACFT IS ALIGNED ON RWY AND HDG READ OFF OF HSI.