A319 FLT CREW IS DISPATCHED INCORRECTLY AND ACCEPTS THE FLT.

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PREVIOUS DAY THIS CREW FLEW INTO RSW. ILS AND NDB WERE NOTAMED NA OTS. TROPICAL DEPRESSION APCHING RSW. FORECAST WX WAS VFR; HOWEVER; WX CALLED FOR 1 MI +PTSRA AND WINDS VARIABLE 20 KTS GUSTING TO 35 KTS. I CALLED DISPATCH TO ADVISE I DID NOT THINK WE COULD GET IN AND QUESTIONED VIABILITY OF FLT PLAN. DISPATCH WAS NOT AWARE AT ALL; OF ANY NOTAMS. I QUESTIONED IF WE HAD A MORE SUITABLE PROVISIONAL ARPT WITH AN ILS TO FLY TO. DISPATCH ADVISED TPA; FLL; OR MCO OUR ALTERNATE. I ASKED HIM TO LOOK INTO IT FURTHER AND ADVISE US. I EXPLAINED TO HIM ALSO; THAT I DID NOT THINK THE VOR RWY 24 WAS AN OPTION AS THE WINDS PROBABLY WOULD FAVOR RWY 6. ONCE IN THE PLANE; PRIOR TO PUSH; I BEGAN RESEARCHING OPTIONS AND PROVISIONAL ARPTS. I ACARS'ED WX FOR RSW; TPA; FLL; AND MCO. THE FORECAST REMAINED THE SAME. I FAILED TO NOTICE THAT THE VOR WAS ALSO OTS IN THE NOTAM SECTION. ESSENTIALLY UNBEKNOWNST TO US THE ARPT WAS VFR ONLY FOR OUR AIRLINE. 350 NM OUT; NEW WX WAS ACARS'ED SHOWING VFR. ABOUT 40 NM OUT; APCH TRIED TO VECTOR US TO THE RNAV RWY 6 APCH. WE EXPLAINED OUR SITUATION AND REQUESTED HOLDING WHILE WE FORMED A PLAN. ATC WAS IRRITATED AND BEGAN PUSHING US FOR ALTERNATE INFO. WE REQUESTED A VECTOR OVER THE FIELD TO OBSERVE ACTUAL CONDITIONS AND WERE REFUSED. WE ACCEPTED HOLDING INSTRUCTIONS TO LBV 20 NM FROM RSW. I REQUESTED A CLOSER IN HOLD TO OBSERVE THE SITUATION. WE REQUESTED AN RNAV FIX. THE CTLR QUESTIONED WHY WE COULD USE AN RNAV FIX; BUT NOT SHOOT AN RNAV APCH. I EXPLAINED THE SITUATION WITH OUR OPS SPECS; ETC. THEY APPROVED THE ARPT VISUALLY AND WERE GIVEN THE VISUAL APCH. FOM NEEDS SPECIFIC VERBIAGE OUTLINING THIS SCENARIO. ALSO REINFORCE DISPATCHER RESPONSIBILITY IN NOTAM NOTIFICATION. REINFORCE THE SIGNIFICANCE OF OUTLINING POTENTIAL ISSUES LIKE THIS IN THE CREW BRIEF FORM AND RELEASE REMARKS SECTION. THE SQR 5 ARR HAD TO BE NOTAMED OUT FOR ALMOST 2 MONTHS AND EACH TIME I MENTIONED IT TO DISPATCH THEY DID NOT KNOW ABOUT IT. SUPPLEMENTAL INFO FROM ACN 699679: THE CAPT AND MYSELF DID NOT NOTICE THAT THE VORTAC WAS OTS. WHEN THE DISPATCHER INFORMED US OF THIS THAT IS WHEN WE REALIZED THAT WE WERE DISPATCHED ILLEGALLY. PER OUR FOM VOLUME 1; A FLT MAY BE RELEASED TO AN ARPT WHEN THE CURRENT WX RPTS AND FORECAST; OR A COMBINATION THEREOF; INDICATE THAT THE WX WILL BE AT OR ABOVE MINIMUMS AT THE ESTIMATED TIME OF ARR. WITH NO OPERATIVE NAV EQUIP; AND THE FORECASTED WX BEING WHAT IT WAS; WE HAD NO WAY OF SHOOTING AN APCH. WE NEVER SHOULD HAVE BEEN RELEASED TO BEGIN WITH.