UPON LNDG; ACFT TAXIES WITHOUT CLRNC.

Narrative

WE HAD JUST LANDED ON RWY 27L IN ATL; TAXIED OFF THE RWY AND TWR CLRED US TO CROSS RWY 27R AND JOIN TXWY L AND CONTACT GND CTL ON FREQ 121.75. WE DID JUST THAT; BUT WHILE TAXIING DOWN TXWY L; WE TRIED TO CONTACT GND CTL 3 TIMES ONLY TO HAVE OUR XMISSION BLOCKED ALL 3 TIMES. WE CONTINUED TO TAXI; PASSING RAMPS #1 AND #2. GND CTL CLRED AN ACR JET ONTO THE OUTER TXWY IN FRONT OF US. WE STILL HAD NOT TALKED TO GND CTL; BUT WERE CONVERGING WITH THE ACR JET. I STOPPED THE AIRPLANE SHORT OF RAMP #3 AND THEN HEARD GND CTL SAY; 'I AM NOT TALKING TO HIM' MEANING US. WE LET ACR GO IN FRONT OF US AND THEN GND CTL STILL DID NOT ACKNOWLEDGE US; BUT CONTINUED TO TALK TO SOMEONE ELSE. WE PROCEEDED TO TAXI AND UPON REACHING RAMP #3; FINALLY MADE RADIO CONTACT WITH GND CTL AND TOLD HIM WE WERE GOING TO RAMP #4. HE SEEMED A BIT PERTURBED WHEN WE SAID WE TRIED TO REACH HIM 3 TIMES; BUT HE TOLD US TO TAXI TO RAMP #4. OTHER THAN THAT; NOTHING HAPPENED. I MADE THE MISTAKE OF CONTINUING TO TAXI THE AIRPLANE BECAUSE I WAS UNDER THE IMPRESSION THAT MY FO ALREADY CONTACTED GND CTL; THAT IS WHY I CONTINUED TO TAXI. WE JUST CAME OFF A 12 HR DUTY DAY FLYING OVER 7 HRS; SO ALERTNESS AND AWARENESS WAS SLIGHTLY NOT 100 PERCENT. GND CTL NEVER DID ACKNOWLEDGE US EVEN AFTER WE GAVE WAY TO ACR. IN THE FUTURE I WILL PAY MORE ATTN TO WHAT IS BEING SAID ON THE RADIO EVEN WHEN I AM NOT TALKING.