PILOT DEPARTS FROM TXWY M AFTER BEING CLEARED TO TKOF ON RWY 36L AT MEM.

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I WAS ABLE TO MAKE CONTACT WITH GND AFTER 3 ATTEMPTS ON 121.9. IT WAS OBVIOUS THAT THE CTLR WAS HAVING DIFFICULTY WITH SEVERAL ACFT CALLING AT ONCE ON DIFFERENT FREQS BECAUSE THE CTLR REQUESTED THAT ALL ACFT COME UP ON 121.65. I MADE CONTACT AND WAS INSTRUCTED TO TAXI TO RWY 36L VIA TXWY A AND TO HOLD SHORT OF TXWY S. I TAXIED AS INSTRUCTED AND HELD SHORT OF TXWY S AWAITING FURTHER TAXI INSTRUCTIONS. IN A FEW MINS I WAS INSTRUCTED TO CONTINUE TAXIING TO RWY 36L VIA TXWY A THEN N. AS I WAS TAXIING I WAS MONITORING MY PROGRESS ON THE ARPT DIAGRAM ON MY MULTI FUNCTION DISPLAY ON THE PANEL. I HAD ZOOMED IT IN SO AS TO SEE THE TXWY LETTERS BETTER AND COULD ONLY SEE THE TXWY N THAT I WAS ON. I WAS IN TRAIL OF 2 AIRLINERS ALSO TAXIING ON TXWY N. AS I APCHED M3 I SWITCHED OVER AND MONITORED THE TWR ON 128.425. I THOUGHT IT WAS STRANGE THAT THE FREQ WAS SO QUIET. I FIGURED THAT THEY HAD COMBINED FREQS AS GND HAD TO 121.65. AS I TURNED ON M2 AND CAME TO A STOP; I GOT A TFC ALERT ON MY MFD; WHICH BLANKED OUT THE ARPT DIAGRAM. I CALLED TWR; AS I RECALL TWICE; WITH NO REPLY; THEN SWITCHING TO 119.7; CALLING AGAIN WITH NO REPLY; THEN I SWITCHED TO 118.3 AND THE CTLR ADVISED THAT I SHOULD BE ON 128.425. I CONTACTED TWR ON 128.425 AND THE CTLR CLRED ME FOR A RWY 36L DEP. I MUST HAVE ASSUMED THAT I WAS ON TXWY M; BECAUSE I WENT THROUGH THE DEP CHKLIST; PWRED UP; TURNED R ON WHAT I THOUGHT WAS RWY 36L; AND DEPARTED. IF I HAD BROUGHT UP THE ARPT DIAGRAM AGAIN IT WOULD HAVE SHOWN ME THAT I WAS ON TXWY M. I REMEMBER THINKING THE LIGHTS WERE TURNED UP AWFULLY HIGH. WITH DOING THE SPD CHKS; XCHKS; AND LOOKING FOR TFC; I FAILED TO REALIZE THAT I WAS NOT ON RWY 36L. JUST PRIOR TO ROTATE I REALIZED THAT I HAD TXWY LIGHTS ON BOTH SIDES OF ME. I ROTATED AND SIDE STEPPED TO THE RWY AS THE CTLR ADVISED ME THAT I HAD JUST TAKEN OFF FROM THE TXWY. I ACKNOWLEDGED HIS XMISSION. THE CTLR THEN ADVISED THAT HE HAD A NUMBER FOR THE TWR FOR ME TO CALL WHEN I GOT ON THE GND. I WROTE DOWN THE NUMBER AND PROCEEDED TO MY DEST. AFTER LNDG I MADE CONTACT WITH THE SUPVR ON DUTY AT THE MEMPHIS TWR AND IDENTED MYSELF. HE ASKED ME TO CALL BACK ON ANOTHER NUMBER; WHICH I DID. THE SUPVR ANSWERED AND ASKED ME FOR MY NAME; ADDRESS; PHONE NUMBER AND PLT CERTIFICATE NUMBER. HE ASKED ME WHEN I REALIZED THAT I WAS ON THE TXWY DURING TKOF; I SAID JUST BEFORE I ROTATED. HE SAID THAT IT WAS A GOOD THING THAT NO ACFT WAS ON THAT TXWY AT THE TIME. HE ASKED ME IF I SAW A CJ IN THE VICINITY OF M6. I REPLIED THAT I HAD NOT. HE SAID THE INCIDENT HAD BEEN RPTED TO THE FSDO AND THAT SOMEONE WOULD BE CONTACTING ME. THIS IS A PERFECT EXAMPLE OF WHAT I HAVE HEARD IN MANY AVIATION SCHOOLS ABOUT THE SNOWBALL EFFECT. THIS WAS A DAY IN WHICH NOTHING SEEMED TO GO RIGHT. WITH NOTHING GOING RIGHT; SEVERAL DELAYS; LONG DAY; FATIGUE; NOT FEELING WELL; IN A HURRY TO GET HOME; IT ALL ADDED UP TO WHAT COULD HAVE BEEN A VERY FATAL MISTAKE. I ALSO VIOLATED ONE OF MY OWN PERSONAL RULES WHICH IS NO SINGLE PLT OPS IN UNFAMILIAR HIGH DENSITY ARPTS OR IN HVY WX. MY R SEATER WAS ON ANOTHER TRIP AND WAS UNAVAILABLE AND I HAD BEEN IN MEM ON SEVERAL OCCASIONS IN THE PAST BUT HAD NEVER DEPARTED RWY 36L AT NIGHT. I AM ADDING ANOTHER PERSONAL RULE AFTER THIS INCIDENT. THAT IS; NO SINGLE PLT OP OVER 8 HRS DUTY AT NIGHT.