B737-700 ENROUTE OVERWATER EXPERIENCES FMC VNAV ANOMALY AND INDICATIONS OF INSUFFICIENT FUEL UPON ARRIVAL AT THE DEST. RETURNS TO DEP ARPT.

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WHEN THE FLAPS RETRACTED AFTER TKOF; THE TARGET SPD FOR CLB DID NOT CHANGE TO '250/10000.' INSTEAD IT READ '212/FLAPS' OR '210/FLAPS' (IT WOULD CHANGE). AT 3000 FT; I CALLED FOR VNAV AND VNAV WOULD NOT ENGAGE. THE CDU STILL READ '212/FLAPS.' I CONTINUED TO CLB AND WAS CLRED DIRECT CLUTS. LNAV WORKED NORMALLY. I ENGAGED THE AUTOPLT AND ASKED THE FO TO CALL ZZZ MAINT. I BEGAN TO LOOK THROUGH THE CDU PAGES FOR INCORRECT ENTRIES. AFTER THE FO GOT MAINT ON RADIO; I ASKED THE FO TO FLY WHILE I TALKED TO MAINT AND WORKED ON THE PROB. MAINT HAD A DIFFICULT TIME UNDERSTANDING THE ISSUE AND SUGGESTED I SWITCH THE FMC TO BOTH ON 1 AND BOTH ON 2. I DID THIS. THERE WAS NO CHANGE. BOTH FMC'S WERE THE SAME. AN FMC LIGHT ILLUMINATED ON THE L FORWARD PANEL. HOWEVER; NO MESSAGE APPEARED IN THE FMC. WHILE LOOKING FOR DISCREPANCIES AND COMPARING THE 2 CDU'S; I SAW THE FUEL FOR ARR IN OAK CHANGE TO 4.9 ON BOTH CDU'S. TARGET SPDS WERE OFF FOR ALL THE LEGS. INFO THAT WAS NORMALLY AVAILABLE WAS MISSING ON SEVERAL PAGES. WHILE TALKING TO MAINT; I WAS ASKED TO STAND BY AND THEN REALIZED I HAD GOTTEN OUT OF RANGE AND THEY WERE NO LONGER ON THE FREQ. I CALLED COMMERCIAL RADIO AND ASKED FOR A PATCH. MEANWHILE; I WAS CHKING FOR POPPED CIRCUIT BREAKERS; CHKLISTS; MANUALS FOR INFO AND WAITING FOR COMPANY MAINT TO COME BACK ON FREQ. COMPANY MAINT HAD NO SUGGESTIONS EXCEPT A COMPLETE 'REBOOT.' I ASKED IF THERE WAS ANYTHING WE COULD DO INFLT AND DID NOT GET AN ANSWER. I ASKED IF ANYONE IN FLT OPS HAD ANY SUGGESTIONS. I WAS THINKING MAYBE WE HAD OVERLOOKED SOMETHING IN OUR PROGRAMMING AND THE MESSAGE '212/FLAPS' COULD BE SOMETHING SIMPLE THAT WAS LEFT OUT OR NEEDED ADDING. I ALSO ASSUMED INCORRECTLY THAT MAINT WOULD HAVE A WAY TO LOOK UP THIS MESSAGE AND GIVE US SUGGESTIONS INVOLVING THE FLAP LOGIC INTERFACE WITH THE COMPUTER. THE FUEL FOR ARR DROPPED TO 1.1 AND THE 2 CDU'S BEGAN TO DISPLAY DIFFERENT INFO. MAINT AT THE SAME TIME SAID THEY WERE RECOMMENDING A TURN AROUND. WE WERE JUST APCHING CLUTS AND I INFORMED ATC THAT WE WANTED TO RETURN TO ZZZ. WE TURNED AROUND WITH A CLRNC TO ZZZ AND WERE UNABLE TO PROGRAM THE ARR INTO THE FMC. I ASKED FOR A RADAR VECTOR AND EVENTUALLY THE FO GOT THE COMPUTER TO TAKE THE ARR. HOWEVER; THE DISCREPANCIES BTWN BOTH CDU'S WERE INCREASING. BY THE TIME WE WERE DOWNWIND; THE MAP DISPLAY SHOWED 2 PARALLEL RWYS FOR RWY 8L EVEN THOUGH WE HAD PROGRAMMED IN THE ILS TO RWY 8L. WE ADVISED ATC THAT WE WERE UNABLE LAHSO DUE TO AN OVERWT LNDG. WE LANDED WITHOUT INCIDENT. THE MAINT COMPUTER TECHNICIAN WAS UNABLE TO FIND ANY PROB IN THE SYS. THE COMPUTERS WERE FINALLY REBOOTED AND WE HAD NO FURTHER PROBS ON THE FLT.