PA32RT-300T PLT ON IFR APCH HAS DME FAIL AND WHILE TROUBLESHOOTING AND MAINTAINING REQUESTED SPD HE DSNDS BELOW PUBLISHED ALT.

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ON AN IFR FLT PLAN FROM GNV TO NEW; I DIVERTED FROM NEW (WITHOUT MAKING AN APCH) TO MSY BECAUSE NEW WAS RPTING BELOW MINIMUMS; MSY WAS ABOVE MINIMUMS AT 500 FT AND 3 MI VISIBILITY. NEW ORLEANS APCH GAVE ME A DSCNT TO 3000 FT AND VECTORS TO THE MSY ILS RWY 01. NEARING ABART; THEY CLRED ME FOR THE ILS RWY 01 APCH; DSNDING TO 2000 FT UNTIL ESTABLISHED ON THE LOC AND TURNING TO 350 DEGS TO INTERCEPT. APCH ADDED THAT I WAS TO MAINTAIN MY 'PRESENT SPD' UNTIL THE OM. MY 'PRESENT SPD' IN THE DSCNT WAS 165 KTS; EASY FOR A DSNDING LANCE; BUT HARD TO MAINTAIN IN LEVEL FLT AT CRUISE PWR. THERE WAS NEARLY CONTINUOUS MODERATE TURB. AT THIS POINT; THE ILS INDICATOR SEEMED TO BE GIVING NORMAL READINGS FOR THAT PHASE OF THE APCH. MY #1 NAV WAS SET FOR THE ILS. MY #2 NAV WAS SET-UP FOR THE MISSED APCH RADIAL (082 DEGS) OFF RQR. THE MARKER BEACON RECEIVER WAS ACTIVATED; AND I HAD SET THE DME ON I-JFI (THE LOC) SLAVED TO THE #1 NAV; TO IDENT ABART AND TO BACKUP THE IDENT OF THE OM. CONTINUING THE DSCNT AT 165 KTS; I NOTICED THAT I WAS NOT GETTING A READING ON THE DME. I DOUBLE CHKED THE CTL SETTINGS WITHOUT SUCCESS; AND THEN SWITCHED TO ITS INTERNAL FREQ CTL; STILL WITHOUT SUCCESS. WHILE THIS WAS GOING ON; I GOT ESTABLISHED ON THE LOC WITHOUT ANY PROB. I GAVE UP ON THE DME AND THEN NOTICED THAT: 1) THE GS NEEDLE WAS CTRED; BUT THE SIGNAL FLAG WAS RED (INOP); 2) THE ALT WAS APCHING 1000 FT; 3) THE AIRSPD WAS STILL ABOUT 165 KTS; 4) THE OM BEACON WAS JUST COMING IN (ALT MINIMUM 1500 FT); AND 5) THE CEILING WAS FAIRLY RAGGED AND I HAD GND CONTACT MUCH OF THE TIME. I WENT TO CLB PWR AND BROUGHT THE NOSE UP. THE (CLEAN) ACFT STRUGGLED AND CLBED ONLY VERY SLOWLY. IN THE MEANTIME; NEW ORLEANS WARNED ME TO 'WATCH MY ALT.' I ACKNOWLEDGED AND CONTINUED TO TRY TO CLB. I MANAGED TO REACH 1200 FT AND THEN; NOW BEING INSIDE THE MARKER; I CONDUCTED A NORMAL AND UNEVENTFUL LOC APCH AND LNDG (CHARTED MINIMUMS 416 FT AND 1 MI VISIBILITY). COMMENTS: I AM QUITE CONVINCED; FROM THE POOR ACFT PERFORMANCE IN THE ATTEMPTED CLB; THAT WE WERE CAUGHT IN THE GRIP OF A FAIRLY STRONG DOWNDRAFT. THIS WAS THE PRIMARY CAUSE OF THE UNDERSHOOT AND WOULD HAVE RESULTED IN A DSCNT BELOW 1500 FT IN ANY CASE. ALTHOUGH NEITHER THE ACFT ON THE APCH IMMEDIATELY IN FRONT OF ME OR BEHIND RPTED A SHEAR; THEY WERE BOTH TRANSPORT CATEGORY SHIPS; AND THE SHEAR MAY HAVE BEEN SHORT LIVED. I WAS SO BUSY WORKING OUT THE RECOVERY THAT I NEVER CALLED IT IN EITHER. ATC'S INSISTENCE THAT I MAINTAIN A HIGHER THAN LEVEL CRUISE SPD IN THE DSCNT EXACERBATED THE POTENTIAL FOR AN INADVERTENT UNDERSHOOT OF THE GS. I SHOULD HAVE TAKEN EXCEPTION TO THIS REQUEST; BUT I WAS TRYING TO GIVE THEM WHAT THEY WANTED. MY ATTN TO THE DME PROB REDUCED THE TIME AVAILABLE FOR MONITORING THE GS AND ALT; SO I AM NOT SURE HOW LONG THE UNUSUAL DSCNT HAD GONE ON. MY GUESS IS THAT IT WAS LESS THAN A MIN. THE GS RECEIVER HAD FAILED ABOUT A MONTH BEFORE AND HAD BEEN REPAIRED. IT HAD BEEN OPERATING NORMALLY DURING THIS TRIP. I DID THE ILS RWY 28 AT GNV A FEW DAYS BEFORE. THERE IS NO QUESTION THAT THE RECEIVER FAILED AGAIN; EITHER DURING THE APCH ITSELF; OR EARLIER -- WITH TURB-INDUCED NEEDLE MOTION GIVING ME THE FALSE IMPRESSION OF INITIAL FUNCTION (THOUGH I HATE TO THINK THAT I WOULD HAVE MISSED THE RED FLAG). THE DME WAS WORKING FINE BEFORE AND SINCE. I HAVE TO ASSUME THAT IT WAS HAVING A PROB READING A LOC; OR THAT THE LOC DME WAS NOT OPERATING. OF COURSE; THE PLANE HAS GONE TO THE AVIONICS SHOP.