LGT FLC DOES NOT TURN AS VECTORED DUE TO EXTREME WX; DSNDS BELOW ASSIGNED ALT.

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WE WERE CLRED TO 5000 FT MSL FROM 6000 FT. IN THE DSCNT; WE WERE TOLD TO TURN L TO 180 DEGS FOR A BASE LEG AT 'A.' AT LEAST 2 ATTEMPTS WERE MADE BY US TO EXPLAIN THAT THE TURN WOULD PLACE OUR ACFT IN 1 OF 2 STRONG (RED) ECHO RETURNS; AND THAT WE HAD TO DELAY THE TURN. DUE TO EXTREMELY HVY RADIO WORK; THE CTLR COULD NOT RECEIVE OUR MESSAGE. IN THE PREOCCUPATION AND FRUSTRATION WITH NOT BEING ABLE TO COMPLY WITH ATC'S CLRNC TO TURN; IN CONJUNCTION WITH THE OBVIOUS SAFETY CONCERNS OF TAKING MY ACFT INTENTIONALLY THROUGH AN AREA OF STRONG ECHO RADAR RETURNS; WE DSNDED TO 4480 FT MSL; 520 FT BELOW OUR CLRNC OF 5000 FT. RETURN TO 5000 FT OCCURRED WITHIN 15 SECONDS OF THE CREW NOTICING THE ALT. THE EFFECT OF THE ALT ALERTING SYS WAS GREATLY SUBDUED NOT ONLY BECAUSE OF PREOCCUPATION WITH SEVERE WX; BUT BECAUSE OF A NUMBER OF STEP-DOWN DIRECTIVES FROM ATC IN QUICK SUCCESSION (7000 FT TO 6000 FT TO 5000 FT; ETC). RADIO CONTACT WITH APCH CTL WAS RE-ESTABLISHED AT 'B.' AT THIS POINT WE HEARD A PIREP FROM THE ACFT AHEAD OF US ON APCH TO RWY 8L INDICATING A 'FAIRLY SMOOTH RIDE.' WE IMMEDIATELY COMPLIED WITH THE TURN TO 180 DEGS; USING 30 DEGS BANK AT 170 KTS (WHICH I BELIEVE WAS OUR CLRED AIRSPD). THE TURN TOOK US THROUGH THE YELLOW/GREEN ECHO RETURN OF THE LARGER STORM WHERE WE EXPERIENCED LIGHT RAIN AND LIGHT TURB. THE APCH PATH FOR THE PARALLEL RWY 9R WAS NOT ENCROACHED UPON. SPECIAL NOTE: THIS PLT EXPERIENCED A LIGHTNING STRIKE ON FLT DEN-ABQ; WHICH DAMAGED THE AUTOPLT. THIS OCCURRED IN AN AREA OF 'GREEN' RADAR RETURNS.