A B737-500 FLT CREW IS CLRED ONTO A CLOSED RAMP BY RAMP TWR.

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FLT LANDED IN DEN. AFTER EXITING RWY 16L; OUR TAXI INSTRUCTIONS WERE TO PROCEED TO GATE VIA TXWY F AND ENTER THE RAMP AT TXWY C SOUTH. AS WE APCHED THE RAMP AREA; I MONITORED GND CTL WHILE THE FO CONTACTED RAMP TWR. THE FO SAID RAMP HAD CLRED US IN ON TXWY BN. I REALIZED THIS WAS NOT THE NORMAL WESTERN RAMP ENTRY POINT; BUT ASSUMED THE 'SHORT-CUT' CLRNC WAS DUE TO THE LATE HR AND NO OTHER ACFT ON THE RAMP. AFTER WE WERE ESTABLISHED ON TXWY BN; WE NOTICED CONSTRUCTION CONES AHEAD ON THE TAXI LINE. I JOGGED TO THE R (SOUTH) TO AVOID THE CONES AND STOPPED. THE FO MADE REPEATED; UNSUCCESSFUL ATTEMPTS TO CONTACT RAMP TWR. IN LIEU OF INSTRUCTIONS; I MANEUVERED THE ACFT AROUND ANOTHER SET OF CONES AND ENTERED THE RAMP NEAR THE TXWY CS ENTRY POINT. THE FO MADE SEVERAL OTHER UNSUCCESSFUL ATTEMPTS TO CONTACT RAMP TWR AS WE TAXIED TO THE GATE. WE WERE MET AT THE GATE BY AN ARPT OPS OFFICER AND INFORMED THAT WE HAD TAXIED THROUGH A CLOSED AREA. I CONDUCTED A POSTFLT INSPECTION OF THE ACFT WHILE THE OUTBOUND CREW CONDUCTED THEIR PREFLT. NO ACFT DAMAGE WAS NOTED. CONTRIBUTING FACTORS: RAMP TWR'S CLRNC INTO THE CLOSED AREA. THE CONES WERE VERY DIFFICULT TO SEE AND NOT VISIBLE UNTIL ILLUMINATED BY THE ACFT TAXI LIGHT. I BELIEVE ONLY 1 CONE WAS DIMLY LIGHTED. FATIGUE MAY HAVE BEEN POSSIBLE. THIS WAS LATE AT NIGHT; THE END OF A 4-DAY TRIP; AND THE DAY'S FLTS HAD BEEN QUITE DEMANDING DUE TO EXTENSIVE DELAYS AND WX AVOIDANCE.