MLG EXECUTES MAP DUE TO POOR ALIGNMENT WITH RWY CAUSED BY ATC SWITCHING THE ILS.

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ESTABLISHED ON ILS FINAL RWY 17; CAPT AND FO BOTH ON ILS. APPROX 1500-1000 FT MSL FLAGS APPEAR BOTH SIDES; ILS SIGNAL LOST. HAVE GND CONTACT CLRLY; BUT RWY NOT IN SIGHT. CAPT SWITCHED TO LNAV. AT 1000 FT AGL I CALL '1000 FT' NO CONTACT.' CAPT MADE A REF TO GND CONTACT AND CONTINUING; THAT WE SHOULD PICK IT UP SOON. AT APPROX 300 FT WE PICKED UP THE RWY. WE WERE APPROX 3/4 MI OUT AND APPROX 1/2 MI L OF RWY CTRLINE. CAPT ATTEMPTED TO LINE-UP WITH THE RWY UNSUCCESSFULLY. EXECUTED A MISSED APCH AT APPROX 100 FT AGL. VECTORED TO ILS 35 TO UNEVENTFUL LNDG. AFTER MISSED APCH ATC APOLOGIZED FOR INADVERTENTLY SWITCHING THE ILS TO RWY 35 DURING OUR APCH. WE SHOULD HAVE EXECUTED A MISSED APCH AS SOON AS THE ILS SIGNAL WAS LOST. WE BOTH FELT LIKE WE WOULD PICK UP THE RWY MOMENTARILY. THE 'BORDERLINE' WX; FLAT TERRAIN; LNAV BACKUP AND FAMILIARITY WITH THE ARPT ALL MADE IT POSSIBLE TO CONTINUE THE APCH. SHOULD HAVE EXECUTED A MISSED APCH AFTER PICKING UP THE RWY SINCE WE WERE NOT IN A POS TO MAKE NORMAL LNDG DUE TO THE MANEUVERING REQUIRED. I KNOW WHAT WE SHOULD HAVE DONE AND WON'T MAKE THE SAME MISTAKE AGAIN.