AFTER AN ALL NIGHT FLT AND 2 MISSED APCHS BROUGHT ON BY SUN POS; FATIGUE AND DIFFICULTY WITH ACFT SYS AN ACR CREW LANDS AT JFK.

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ON ARR INTO JFK AFTER FLYING ALL NIGHT ON A RED-EYE FLT FROM JFK; WE WERE BEING VECTORED THE VOR RWY 4R APCH. THE VECTOR WAS VFR; BUT THE SUN WAS COMING UP IN THE SAME DIRECTION OF THE APCH; AND IT WAS HARD TO SEE. WE COMMENCED WITH THE APCH. WE WERE UNABLE TO LOCATE THE RWY AND EXECUTED A MISSED APCH. WE GOT VECTORED FOR ANOTHER APCH. DURING THE SECOND APCH; (THE A320 ACFT BUILDS A GLIDE PATH FOR A VOR APCH; AND IS COUPLED TO THE AUTOPLT) WHEN REACHING THE FAF; THE ACFT DIDN'T START TO DSND TO THE MDA; IT JUST FLEW STRAIGHT AND LEVEL AT 1500 FT (THE INITIAL ALT). AFTER A 1 MI OR 2; IT BECAME CLR; THE APCH WASN'T GOING TO WORK OUT. WE PROCEEDED TO EXECUTE A MISSED APCH. TWR GAVE US MISSED APCH INSTRUCTIONS CLB TO 2000 FT AND TURN 110 DEG HDG. THE HEADING FOR THE APCH IS 040 DEGS. WE MISINTERPED THE INSTRUCTIONS AND THOUGHT HE SAID 010 DEGS AND TURNED TO THAT HEADING. AFTER A FEW MINS ATC ASKED WHAT WE WERE DOING AND TOLD US TO TURN TO 110 DEG HDG. WE THEN DID; AND ASKED FOR VECTORS FOR AN ILS APCH AND LANDED WITHOUT FURTHER INCIDENT. FATIGUE PLAYED A FACTOR IN THE MISCOM; ACCOMPANIED WITH THE FACT IT WAS THE SECOND MISSED APCH; AND THERE WAS A CLB OF ONLY 500 FT FROM WHERE WE WERE AT AND THE ALT WE HAD TO CLB TO; WAS A SHORT TIME TO CLEAN UP THE ACFT. ALSO; WITH THE ACFT NOT DSNDING WHEN IT SHOULD HAVE; AND TRYING TO FIGURE OUT WHY; WAS ALSO DISTRACTING. AS SOON AS ATC ADVISED US OF THE HEADING WE SHOULD HAVE BEEN ON; WE TURNED TO IT; AND THE SAFETY OF THE FLT WAS NEVER COMPROMISED.