B737 FLT CREW DEPARTS SJC WITH BOTH FMCS INOPERATIVE AND QUICKLY DISCOVERS THAT THEY HAVE BECOME FMC DEPENDENT.

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DURING PREFLT AT SJC ON A TURN; THE FMC WOULDN'T PROGRAM AND PROVIDE A MAGENTA COURSE LINE FOR ANYTHING. MAINT WAS CONTACTED AND BOTH FMC'S WERE MEL'ED. WE TOOK OUR TIME PREPARING FOR THE DEP AS WE HAD TO MANUALLY LOOK UP AND INPUT ALL SPDS; PWR SETTINGS; ETC; PRIOR TO DEP; PER THE MEL. WE BRIEFED THE DEP AND HOW IT WOULD BE FLOWN RAW DATA WITHOUT THE FMC'S. THE MEL ALLOWED FOR THE AUTOTHROTTLES TO BE TURNED ON AFTER 1000 FT AGL. ALL WAS FINE UNTIL THE TURN AT 1.8 DME TO 120 DEG MAGNETIC HDG WHICH WAS ALSO WHERE ATC WAS TALKING TO US AND THE AUTOTHROTTLES WERE TURNED ON; ALL WHILE FOLLOWING PROFILE AND CLEANING UP WHILE HAND FLYING. DURING ALL THIS THE HDG BUG WAS INADVERTENTLY MOVED TO 070 DEGS VICE 120 DEGS AS THE CAPT WAS INTERRUPTED BY ATC DURING THE CHANGE. AS I MADE THE TURN; THE AUTOTHROTTLES WERE COMMANDING FULL PWR AND IT WASN'T REQUIRED AS WE CAN ONLY CLB TO 5000 FT MSL UNTIL THE 047 DEG RADIAL OFF SJC VOR. AS VERT SPD MODE WAS SELECTED TO 1500 FPM AND I LOWERED THE NOSE; THE EXCESSIVE PWR BECAME OBVIOUS AS THE AIRPLANE ACCELERATED RAPIDLY; TAKING ALL MY ATTN AS THE CAPT WAS LOOKING FOR TFC. I DISCONNECTED THE AUTOTHROTTLES; RESUMED MANUAL THROTTLE CTL AND ROLLED OUT ON THE HDG BUG NOT NOTICING THAT IT WAS ON 070 DEGS NOT 120 DEGS BECAUSE OF THE WORKLOAD. I LOOKED OUTSIDE AND REALIZED WE WERE HDG OFF-COURSE JUST AS ATC TOLD US TO KEEP THE TURN TIGHT; SO I CORRECTED TOWARD 120 DEGS AND THEY GAVE US 180 DEG HDG WHICH WE COMPLIED WITH. FROM THAT POINT FORWARD ALL RESUMED TO NORMAL SPD AND NO FURTHER EVENTS OCCURRED. ATC MADE NO INDICATION OF BEING UNHAPPY AND THERE WAS NO TFC OR TERRAIN CONFLICTS. THIS HDG ERROR WAS FOR A VERY SHORT TIME AND WAS CORRECTED RAPIDLY. THE BIGGEST THREATS WERE THE DUAL FMC MEL AND THE EXCESSIVE AUTOTHROTTLE INPUTS THAT WERE NEITHER WARNED ABOUT OR EXPECTED. COMMANDING WHAT MUST HAVE BEEN LIMIT PWR (NO LIMITS EXCEEDED) FOR THE CLB; IT DOESN'T CHANGE WHEN A REDUCED CLB RATE AND PWR ARE SELECTED VIA VERT SPD MODE. THIS CAUSED MY SPD TO INCREASE AND THE EFFORTS TO KEEP IT UNDER CLEAN MANEUVERING SPD; PER REGS AND THE FOM; HAD MY FULL ATTN; KEEPING ME FROM NOTICING THE HDG ERROR. THE CAPT WAS ALSO DEALING WITH THREATS OF ATC INSTRUCTIONS AND TFC RPTS; AS WELL AS THE AUTOTHROTTLES. I THINK THE MEL SHOULD SPECIFY THAT THE AUTOTHROTTLES DON'T OPERATE THE SAME AS NORMAL UNDER THIS MEL; AS I THINK THAT THEY WERE THE PRIMARY CAUSE OF THIS EVENT. KNOWING BEFORE HAND THAT THEY WOULD STAY AT LIMIT SETTING WOULD ALLOW ONE TO PREPARE FOR IT OR AVOID IT ALL TOGETHER BY NOT ACTIVATING THE AUTOTHROTTLES UNTIL WORKLOAD DECREASES OR CLB IS STABILIZED. EVEN BY REDUCING THE AUTOMATION AS QUICK AS WE DID; BY TURNING THE AUTOTHROTTLES OFF; TOO MUCH ATTN WAS STILL TAKEN HAVING TO RETURN THE PWR TO A NORMAL LEVEL AND BECAUSE OF THAT; MY SCAN WAS DEGRADED TO NOT LOOK PAST THE HDG BUG AND SEE THAT IT WAS ON AN INCORRECT HDG. THIS MEL TAKES A CREW TO A TOTALLY DIFFERENT NAV TYPE THAT ISN'T FREQUENTLY USED. I DON'T THINK AUTOPLT WOULD HAVE NECESSARILY HELPED AS MORE AUTOMATION PROBABLY WOULD HAVE BEEN WORSE.