FLC OF AN LTT TURBOPROP DURING AN ILS APCH DECLARED AN EMER AFTER THE #1 ENG FEATHERED DURING PWR UP FOR A GAR IN RESPONSE TO TCASII RA.

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I WAS THE COPLT ON FLT TO IND. THERE WAS RPTED RAIN SHOWERS AND STORMS ON ARR. WE HAD A WX RADAR INOP; IT WAS MEL'ED. THE FLT WAS NORMAL ON THE WAY OVER. WHEN WE WERE HANDED OFF TO IND APCH; WE ASKED FOR WX ADVISORIES AND EXPLAINED WE HAD AN INOP RADAR. WE RECEIVED A VECTOR TO JOIN THE ILS APCH. ATC EXPLAINED THAT THERE WOULD ONLY BE RAIN SHOWERS BTWN US AND THE ARPT. WE JOINED THE LOC AND WENT IMC. MY FORWARD LOOKING VISIBILITY WAS ZERO; BUT I COULD SEE OUT MY SIDE WINDOW ABOUT 3/4 OF A MI. WE CROSSED THE MARKER INBOUND; CONFIGURED THE ACFT; AND BEGAN AN ESTABLISHED ILS APCH. AS WE PASSED THROUGH 1100 FT MSL; THERE WAS NO IMPROVEMENT IN THE WX; AND WE HAD A TA FROM TCASII CALLING TFC. WE COULDN'T GET THE VISUAL; AND THERE WAS NO WORD FROM ATC. THE TA QUICKLY TURNED INTO AN RA AND THE TCASII WAS CALLING FOR A CLB OF 2000 FPM. THE GAR WAS INITIATED; AND AS THE PWR WAS APPLIED AND THE NOSE PITCHED UP; THE EEC FAILED ON THE #1 ENG CAUSING THE AUTOFEATHER TO FEATHER #1 ON THE GAR. I DECLARED AN EMER IMMEDIATELY AND WE BEGAN OUR SINGLE ENG GAR PROCS. AS WE BEGAN A R TURN IN THE CLB TO GET OFF THE APCH (WE RECEIVED A VECTOR FROM ATC); I SAW THE TFC PASS BELOW AND TO THE R. IT WAS A C172 BANNER TOW. ON OUR HDG; WE PERFORMED THE QRH FOR PRECAUTIONARY ENG SHUTDOWN AND SINGLE ENG LNDG. THE EMER WAS HANDLED ACCORDING TO THE CHKLIST AND WE WERE VECTORED AROUND FOR A SINGLE ENG ILS. AS WE MADE THE TURN; THE WX HAD CLRED AND THE ARPT WAS IN SIGHT WITH 6 MI VISIBILITY. THE LNDG AND THE TAXI WAS NORMAL AND THE FIRE TRUCKS WERE ON STANDBY. WE PULLED IN TO THE GATE AND RELEASED THE PAX NORMALLY.