A PA32 PILOT DEPARTED A WRONG RWY AFTER BEING RUSHED FOR TKOF; NOT COPYING ATIS COMPLETELY; AND FAILING TO ASK FOR THE RWY.

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IT WAS AN IFR FLT IN VMC FROM RDU WITH A DEP TIME OF APPROX XA00 LCL TIME. I ACQUIRED THE ATIS AND PROCEEDED WITH MY IFR CLRNC. AFTER RECEIVING CLRNC; I SWITCHED OVER TO GND TO RECEIVE MY TAXI CLRNC. I WAS INSTRUCTED BY THE GND CTLR TO TAXI FOR AN INTXN DEP WITHOUT ANY PROMPTING FROM ME. I TAXIED AS INSTRUCTED FOR THE DEP AND UPON REACHING THE RWY WAS INSTRUCTED TO 'FLY RWY HDG; CLRED FOR TKOF AT INTXN C.' I FORGOT WHICH RWY WAS IN USE SO I REFED THE WINDS I HAD RECEIVED FROM THE ATIS INSTEAD OF THE RWY WHICH I SHOULD HAVE USED. SINCE THE RWY WAS 5L/23R AND THE WINDS WERE FROM 290 DEGS AT 9 KTS; I ASSUMED RWY 23R WAS IN USE BUT DID NOT CLARIFY. I DEPARTED THE WRONG RWY AND WAS NOTIFIED OF MY MISTAKE AFTER BECOMING AIRBORNE. NO OTHER AIRPLANES WERE IN THE AREA. CONTRIBUTING FACTORS INCLUDE STRESS DERIVED FROM BEING RUSHED FOR TKOF; LACK OF ARPT INFO; AND MISCOM. BEING RUSHED FOR TKOF CAUSED ME TO WRITE DOWN AN INCOMPLETE ATIS; WHICH RESULTED IN THE LACK OF INFO; MORE SPECIFICALLY THE RWY IN USE. MY CORRECTIVE ACTIONS INCLUDE WRITING DOWN THE ENTIRE ATIS TO CONFIRM THE ACTIVE RWY WHILE MAINTAINING VIGILANCE WITH TAXI AND TKOF CLRNC.