C560 CAPT REPORTED TCAS RA EVENT DURING HOLDING AT 15;000 WITH ZNY INBOUND TO HPN; OPERROR RECORDED WITH N90 TRACON.

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THIS PROB RESULTED DUE TO ATC ISSUES AND SATURATION. WE WERE ON THE BOUNO ARR TO HPN AT 15000 FT AND THE CTLR ADVISED US TO REVERSE COURSE TO A HDG OF 180 DEGS AFTER XING THE DPK VOR (WE WERE ABOUT 5 MI FROM THE VOR WHEN WE RECEIVED THE INSTRUCTIONS). THE CTLR ISSUED HOLDING INSTRUCTIONS ABOUT 3 MINS LATER: HOLD S OF DPK ON INBOUND RADIAL OF ARR. (I BELIEVE IT WAS A 027 DEG COURSE) WITH R TURNS AND 10 MI LEGS; EFC OF 2330. WE PROGRAMMED THE BOX AND PROCEEDED BACK TO THE VOR AS CLRED TO HOLD. ABOUT 3 MI FROM THE VOR; WE NOTICED AN ACFT CLBING AND HEADING TOWARDS DPK. THE ACFT DID NOT LEVEL OFF AND WE RECEIVED A TCAS RA TO DSND. THE FO DID AN EXCELLENT JOB MAKING A SMOOTH; CTLED DSCNT VIA THE TCAS INSTRUCTIONS. I ADVISED ATC THAT WE WERE IN A TCAS DSCNT FOR TFC. WE PICKED UP THE ACFT VISUALLY; AND IT WAS RATHER CLOSE FOR COMFORT. WE PROBABLY WERE WITHIN 1 MI AND THE OTHER ACFT WENT RIGHT THROUGH OUR ALT. WE ENDED UP DSNDING TO 14200 FT AND THEN BEGAN A CLB BACK TO 15000 FT (I ADVISED ATC ONCE AGAIN THAT WE HAD PERFORMED A TCAS DSCNT TO 14200 FT AND WERE CLBING BACK TO 15000 FT). THE CTLR THEN ISSUES AN IMMEDIATE R TURN AND INDICATED 'I DO NOT KNOW WHAT DEP JUST DID TO ME; WE WILL LOOK INTO IT.' THE CTLR WAS VERY BUSY AT THE TIME. HE WAS ISSUING OTHER ACFT NEW CLRNCS BECAUSE ZDC HAD LOST SOME RADAR CAPABILITY. HE ALSO INFORMED US THAT HPN HAD STOPPED TAKING ARRS DUE TO A RADAR OR COM OUTAGE -- HE WAS NOT SURE WHICH. WE WERE REISSUED A CLRNC TO CROSS DPK AND PROCEED ON THE ARR. I HAVE NO SUGGESTIONS ON HOW THIS COULD HAVE BEEN PREVENTED. IT IS A CLASSIC CASE FOR WHY TCAS IS SUCH A GREAT SAFETY FEATURE. IT WAS DUSK; AND WE DID NOT SEE THE ACFT UNTIL THE TCAS ALERTED US.