B737-400 FLT CREW ENCOUNTERS MULTIPLE FMS/AUTOFLIGHT FAILURES ON APCH TO JNU.

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I WAS FLYING TO JNU. PLANNED FOR AND BRIEFED RNP RWY 8 ZULU APCH JNU; WITH AN LDA 8 BACKUP. NORMAL DSCNT WITH ZAN. CLRED FOR THE RNP APCH. AT CUSHI BELOW 10000 FT; GOT A 'SINGLE FMC OPS' MESSAGE; ALONG WITH 'MAP' FLAG. I LOST RNP CAPABILITY ON THE R SIDE AND XFERRED ACFT CTL TO CAPT. AT THAT POINT; WE HAD ONLY A SINGLE FAILURE. HE ATTEMPTED TO RESUME RNP APCH; BUT WE HAD TOTAL MCP FAILURE (50000; ALL DIGITS LIT; LOCKED UP; ETC). WE REVERTED TO OUR BRIEFED BACKUP; THE LDA APCH; WHILE HE REFED HIS MAP. WX WAS SUFFICIENT FOR LDA. IN THE MEANTIME I PLACED FMC SWITCH TO 'BOTH ON L.' RESTORED DUAL FMC OPS SO I HAD A MAP AGAIN. CAPT STAYED ON MAP; I STAYED ON LDA RAW DATA AND XCHKED OUR POS WITH COURSE AND DME. IT WAS QUESTIONABLE WHETHER GPS AND MAP WERE ACCURATE; AS WE SAW DEV ON LDA COURSE INDICATOR; SO WE REVERTED TO NAVING SOLELY ON LDA COURSE. IN THE MEANTIME; WE HAD MCP FLASHING; ALT ALERT FLASHING; ALT HORN HONKING; 20 KT XWIND; ICING. IN THE BACKGROUND; I HEARD ZAN HAND US OFF TO JNU RADIO. WE WERE TOO BUSY TO TALK TO ANYONE; JUST FOCUSED ON STAYING ON COURSE; AIRSPD; CONFIGURING; ETC. AT ABOUT THE SAME TIME; AT APPROX 5000 FT WE SAW VASI/ARPT ENVIRONMENT. THERE WAS NO OTHER TFC IN THE AREA. DECIDED FIRMLY TO CONTINUE FOR LNDG AT THAT POINT. I CALLED OUT DEVS FOR COURSE; AIRSPD; POS; DOUBLE-CHKED CONFIGN; WHAT OUR AIRSPD SHOULD BE; ETC. (WE COULDN'T SET ALTS OR AIRSPDS DUE TO MCP FAILURE.) LANDED WITHOUT INCIDENT IN A MOSTLY HEADWIND APPROX 9 KTS. GOOD BRAKING ACTION. AS WE CLRED THE RWY; I CALLED JNU RADIO AND SAID WE WERE DOWN AND CLR. JNU RADIO ADVISED US TO PLEASE CALL WHEN AT BARLO NEXT TIME. I REPLIED THAT WE HAD SOME PROBS WITH THE ACFT AND DIDN'T HAVE TIME. AFTER ARRIVING AT THE FREIGHT AREA IN JNU; THE MECHS RELAYED THAT THE ACFT HAD BEEN STRUCK BY LIGHTING A FEW DAYS AGO AND HAD EXPERIENCED THE SAME ANOMALIES THAT WE DID. WROTE UP ALL FAILURES; BRIEFED ONCOMING CREW AND WENT TO THE HOTEL. THE COMPANY SHOULD DO A BETTER JOB OF MAINTAINING/CHKING OUR ACFT AFTER SIGNIFICANT EVENTS (LIGHTING PLUS NAV FAILURE). I SHOULD HAVE BEEN ABLE TO SQUEEZE IN A RADIO CALL TO JNU FSS SOMEWHERE; BUT I WAS SO INTENT ON CONFIRMING OUR COURSE INTO JNU (LOTS OF MOUNTAINS IN OUR WAY!) AND ALT; THAT I USED ALL MY RESOURCES. THE ALL-NIGHTER FLYING IS SIMILAR IN EFFECT TO SLIGHT INTOXICATION; IT'S NOT THE SAFEST OP; EVEN WITH PROPER REST. IF WE HADN'T GOTTEN ESTABLISHED; IF WX WAS WORSE; IF HADN'T SEEN LIGHTS; WE'D HAVE GONE MISSED AND CLBED OUT OF JNU. IT DIDN'T SEEM WORTHY OF AN 'EMER' CALL.