MD80 CREW MISSED THE CLRED TXWY ON TAXI IN AT DFW.

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ON LNDG AT DFW; RWY 17C; AFTER EXITING ON TXWY M3; TWR CLRED FLT TO CROSS RWY 17R ON TXWY EL AND CONTACT GND ON 121.65. GND INSTRUCTED CREW TO TURN L ON TXWY L AND TAXI TO THE SW HOLD PAD. AS WE STARTED OUR L TURN; GND INSTRUCTED US TO FIND A TAXIING ACFT ON THE R OF OUR ACFT THAT WAS REVERSING HIS TAXI DIRECTION (N TO S); TO GO TO THE HOLD PAD AND TO NOW FOLLOW THAT TFC TO THE PAD. I IMMEDIATELY STOPPED MY 'AFTER LNDG AND TAXI' CHKLIST; AND TRIED TO ACQUIRE THE GND TFC. BEING SUCCESSFUL; I TURNED BACK TO MONITOR THE PROGRESS OF OUR TAXI; AND IMMEDIATELY REALIZED THAT WE HAD TURNED THE ACFT 135 DEGS INSTEAD OF THE 90 DEGS REQUIRED TO END UP ON TXWY L. WE WERE FACING SW ON TXWY L. WE IMMEDIATELY STOPPED THE ACFT SHORT OF THE RWY AND TOLD GND WE HAD INADVERTENTLY TURNED ONTO TXWY L4. HE IMMEDIATELY CLRED US TO TAXI ONTO RWY 17R; TAXI S AND EXIT BACK ONTO TXWY L; THEN PROCEED TO THE SW HOLD PAD -- WHICH WE DID WITH NO FURTHER EVENTS. THE WX WAS CLR; AND THE LIGHTS ON THE AIRFIELD APPEARED TO BE AT HIGH INTENSITY.