AN MD88 PIC TAXIES TO THE WRONG RWY FOR TKOF AT RNO AFTER BEING DISTR WITH TAXI PROBS AND A RWY CHANGE.

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MUCH CONFUSION ON PUSHBACK INTO ALLEYWAY AT IND. GND CLRED US TO PUSH AND ALSO CLRED A B727 TO TAXI TO A GATE WHICH WE BLOCKED ON PUSHBACK. THE B727 WAS ALREADY INTO THE ALLEY AND COULD NEITHER CLR US TO GET TO HIS GATE NOR TURN AROUND. WE COULD NOT CLR THE B727. GND THEN SAID HE COULD NOT SEE OUR ACFT OR THE ALLEYWAY FROM HIS POS. WE PULLED BACK INTO THE GATE AREA AND EVERYONE SUBSEQUENTLY WAS ABLE TO PROCEED (THAT TOOK ALMOST 15 MINS TO SORT OUT). AS PART OF THE BEFORE START CHKLIST; WE BRIEFED A DEP USING RWY 23L. ATIS CALLED FOR DEP ON RWY 23L&R. WE ACKNOWLEDGED A TAXI CLRNC TO RWY 23R VIA TXWY G AND P. PREOCCUPIED WITH TAXI; ENG START; AND CHK OF WT AND BAL NUMBERS FOR RWY 23R; I TURNED L ON TXWY P VICE R. WE WERE SWITCHED TO IND TWR AND WERE CLRED FOR TKOF. STILL SHORT OF THE HOLD SHORT LINE FOR RWY 23L; I REALIZED OUR MISTAKE. I CALLED TWR FOR CLRNC TO TKOF ON RWY 23L AND RECEIVED SAME. INFLUENCING FACTORS: 1) EARLY MORNING PICK UP (XA40). 2) ATIS GAVE BOTH RWYS FOR DEP. 3) BEFORE START CHKLIST MUST BE COMPLETE BEFORE PUSHBACK. WE CHOSE RWY 23L AS MOST LIKELY RWY AND BRIEFED SUCH ON BEFORE START CHKS. 4) TAXI RTE ASSIGNED (TXWY P) GOES TO BOTH RWY 23L AND RWY 23R. 5) WE HURRIED TO CHK WT AND BAL FOR RWY 23R; HAVING USED RWY 23L NUMBERS TO PROGRAM FMS AND START R ENG. I JUST TURNED THE WRONG WAY WHEN REACHING TXWY P.