RADIO FAILURE ON INST APCH IN IMC. AFTER LNDG TAXI WITHOUT CLRNC LIGHTS FROM TWR.

Narrative

ACFT RADIO WAS STOLEN 3 WKS AGO AND REPLACED WITH A 'NEW' RADIO. RADIO VOLUME WAS BELOW FORMER VOLUME OUTPUT AND COULD NOT BE HEARD AT HIGHEST VOLUME LEVEL AT HIGH RPM ENG SETTING (ON SPEAKER). SINCE I HAD A HEADSET; I PLUGGED IT IN AND HANDLED COMS WHILE MY INST STUDENT FLEW THE AIRPLANE. ALL SEEMED TO WORK FINE ON THE ROUND-ROBIN INST FLT OTHERWISE UNTIL ESTABLISHED ON THE LOC AND CLRED FOR THE ILS TO THE ARPT OF ORIGIN. AT THE OUTER COMPASS LOCATOR RADIO FREQ DIGITAL DISPLAY BEGAN TO FLICKER AND BACKGND NOISE OF STATIC HEARD ON HEADSET AS THE 'BRAND NEW' RADIO TOTALLY FAILED. FREQ DISPLAY WENT HAYWIRE WITH NOTHING THAT RESEMBLED A LEGIBLE 4 DIGIT FREQ FLASHING NONSENSE VIA LIQUID CRYSTAL. I CHKED CIRCUIT BREAKERS -- ALL OK. TURNED RADIO ON AND OFF; EVEN CYCLING MASTER DID NO GOOD. PUSHING ON THE RADIO DID NOTHING -- IT WAS GONE. I SQUAWKED 7700 FOR 1 MIN AND THEN 7600. I XMITTED IN THE BLIND THAT I WAS 'LOST COM' AND CONTINUING ON APCH. WE WERE IN ACTUAL IMC CONDITIONS IN CLOUD; FOG; AND HAZE. NEITHER MY STUDENT REMEMBERS NOR I REMEMBERED AN OFF FLAG ON #1 NAV DISPLAY; ALTHOUGH NEEDLES WERE PERFECTLY CENTERED. SINCE WE WERE ESTABLISHED WE REMAINED ON HDG AND RATE OF DSCNT. WE BROKE OUT ON ABOUT 1 1/2 MI FINAL WHERE WE SHOULD BE. WE FLEW THE APCH AT THE TOP OF GREEN ARC SINCE CTLR REQUESTED BEST FORWARD SPD. WE COULD HEAR APCH CTLR SLOWING NUMEROUS ACRS BEHIND US IN SEQUENCE BEFORE FAILURE. I LANDED WITHOUT VERBAL LNDG OR LIGHT SIGNAL LNDG CLRNC; TAXIED OFF ACTIVE AT CLOSEST INTXN; STILL NO LIGHT FROM TWR; TAXIED TO RAMP ACROSS TAXIWAY WITHOUT TAXI CLRNC OR LIGHT. WE STOPPED ON RAMP NORMALLY REQUIRING CITY AUTHORIZATION OR PRIOR PERMISSION. WE THEN SAW RED LIGHT FROM TWR. OPS VEHICLE THEN ESCORTED TO GA PARKING. I SHOULD HAVE HELD SHORT OF TAXIWAY OFF RWY UNTIL LIGHT SIGNAL OR ESCORT. I WAS IN TOO BIG A HURRY AND SHOULD HAVE CALMED DOWN ON THE GND. I VIVIDLY IMAGINED THE BIG METAL BEARING DOWN ON US AND ALL MY LOGIC AND REASON DAMAGED BY THINKING TOO MUCH BEHIND THE ACFT; RATHER THAN WHAT WAS IN FRONT OF ME. IT DIDN'T HAPPEN (THE FAILURE) WHILE ON VECTORS PRIOR TO APCH. #2 NAV WAS INOP.