DH8D OVERSHOT LEVELOFF WHILE BEING VECTORED FOR APCH; TRIGGERING LOW ALT ALERT AND EGPWS WARNING. FLT CREW EXECUTED PULL-UP; BUT THE FLT DIRECTOR AND AUTOPILOT COULD NOT BE ENGAGED. A RAW DATA APCH WAS FLOWN.

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I WAS THE CAPT AND PLT MONITORING; THE FO WAS THE PF. THE WX WAS IMC AND ZZZ WAS RPTING 2 MI VISIBILITY AND 300 OVCST. WE WERE RECEIVING VECTORS FOR THE ILS 1L. THE AUTOPLT WAS ON AND WE WERE DSNDING TO 3000 FT. AS THE ACFT WAS LEVELING AT 3000 FT; THE FLT ATTENDANTS CALLED WITH AN EMER. I ADVISED THE FO I WAS 'OFF ONE' AND HE ADVISED HE 'HAD ONE.' I THEN SWITCHED TO THE INTERCOM AND SPOKE TO THE FLT ATTENDANT. SHE ADVISED THAT THEY HAD A PAX THAT WAS HAVING A HEART ATTACK OR STROKE AND SHE NEEDED MEDICAL ATTN. I ADVISED THE FLT ATTENDANT WE WERE JUST STARTING THE APCH AND WOULD HAVE MEDICAL STANDING BY. AT THAT MOMENT; ATC CALLED WITH A LOW ALT ALERT. I LOOKED UP AND SAW WE WERE DSNDING THROUGH 2000 FT. THEN THE EGPWS GAVE A TERRAIN AND PULL UP WARNING. I IMMEDIATELY TOOK THE CTLS AND WITH THE FO WE STARTED A RAPID CLB BACK TO 3000 FT; OVERSHOOTING BY 200 FT. ATC CALLED AND ASKED OUR ALT AND I ADVISED THEM THAT WE WERE AT 3200 FT. ATC ADVISED TO TURN TO A HDG OF 030 DEGS AND MAINTAIN 3000 FT; CLRED FOR THE ILS 1L. AT THAT POINT I ACKNOWLEDGED THE CLRNC AND DECLARED AN EMER AND REQUESTED MEDICAL. AT THIS POINT; I COULD NOT CLEARLY SEE MY PFD DISPLAY; IT HAD GONE TO 1/2 BRIGHTNESS. I HAD TO DO A MANUAL REVERSION TO THE MFD DISPLAY AND LOST MY MAP FUNCTION. THE FO WAS HAND FLYING THE ACFT AND I TRIED TO RESET THE FLT DIRECTOR AND THE AUTOPLT. THE FLT DIRECTOR WAS INDICATING A TURN IN THE WRONG DIRECTION AND A CLB WHILE WE WERE LEVEL. THE FO WAS HAVING A DIFFICULT TIME STAYING COORD AND WAS OVERCORRECTING BASED ON THE RAW DATA. I TRIED TWICE TO RESET THE SYS AND IT WOULD NOT. I THEN STOOD BY THE FLT DIRECTOR AND ADVISED THE FO TO FLY RAW DATA. WE THEN FLEW THE REMAINDER OF THE ILS WITH RAW DATA. ON THE GND; WE DISCUSSED THE INCIDENT AND THE FO HAS NO IDEA WHY OR HOW WE MISSED THE ALT. I BELIEVE HE WAS PAYING ATTN TO THE INTERCOM AND NOT FLYING THE AIRPLANE. ONCE THE DEV OCCURRED WITH THE AUTOMATIC DISCONNECT OF THE AUTOPLT DUE TO THE EGPWS IT INHIBITS THE AUTOPLT FOR A PERIOD OF TIME. THE SCREEN HAD BEEN GOING TO DIM FOR SEVERAL DAYS AND NO ONE HAD BROUGHT IT TO THE ATTN OF MAINT. I LEARNED WHEN IT GETS HOT; IT MAY AUTOMATICALLY DIM TO COOL. THE PAX WAS TAKEN TO THE AMBULANCE AND THEN REFUSED MEDICAL ATTN. THE FO HAD ABOUT 15 HRS IN THE PLANE AND 121 ENVIRONMENT. I; AS THE PIC; BECAME DISTR AND FAILED TO KEEP MONITORING OUR FLT PATH. I FALSELY ASSUMED THAT SINCE HE WAS IN THE SEAT HE WOULD HAVE THE DISCIPLINE TO DO HIS SPECIFIC JOB. I NEED TO REMEMBER THAT IN THESE TYPES OF SITUATIONS THE FO MAY NOT HAVE THAT EXPERIENCE AND WILL ALSO BECOME DISTR. IN MY PREFLT BRIEFINGS; I WILL ALWAYS CLEARLY SPELL OUT THE DUTIES OF EACH FLT CREW MEMBER AND EMPHASIZE THE IMPORTANCE OF DOING OUR DUTIES AND THE DISCIPLINE OF NOT BECOMING DISTR. I ALSO NEED TO REMEMBER TO CLOSELY MONITOR ALL ASPECTS OF THE EMER AND REMEMBER TO FLY THE PLANE FIRST. NEVER WILL I FLY A PLANE WITH AN INTERMITTENT PROB THAT COULD AFFECT SAFETY OF FLT. NORMALLY; I WOULD HAVE TAKEN THE CTLS AND FLOWN THE ACFT MYSELF; BUT MY INST DISPLAY PROB DELAYED THAT AND ONCE I REGAINED MY SITUATIONAL AWARENESS A LONG PERIOD OF TIME HAD PASSED AND IT WAS SAFER TO ALLOW THE FO TO CONTINUE SINCE HE HAD CALMED DOWN AND WAS FLYING WITHIN PARAMETERS AGAIN. THE OTHER THING I NOTICED WE ALL GET VERY COMPLACENT WITH HAVING ALL OF THE EQUIP WORKING AND WHEN IT FAILED; WITHOUT PRACTICE; OUR INST SKILLS ARE RUSTY AT BEST. I WILL PRACTICE MORE AT FLYING THE GAUGES AND NOT ASSUME THAT THE FLT DIRECTOR WILL NEVER FAIL. ON THE GND; A RESET OF ALL THE SYS WAS DONE AND THE FLT DIRECTORS AND AUTOPLT RETURNED TO NORMAL OP.