A B737-300 WAS DISPATCHED IN NON COMPLIANCE WITH CTR TANK FUEL EXCEEDING INOP FUEL QUANTITY INDICATOR LIMITS.

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FLT PLANNED FOR OUR LEG ZZZ-ORD. DUE TO CHANCE OF TSTMS IN CHICAGO AREA; WE NEEDED TWO ALTERNATES; NAMELY MKE AND MSP. THIS REQUIRED FULL FUEL ON OUR B737 FOR THE PLANNED 3 HR 39 MIN FLT PLUS RESERVES. ARRIVING AT THE ACFT; FUELER INFORMED ME HE WAS HAVING TROUBLE WITH CTR TANK QUANTITY INDICATOR; NAMELY THAT HE WAS DELIVERING FUEL; BUT GAUGE WOULD NOT READ HIGHER THAN 15400 LBS. OUR TOTAL FUEL LOAD FOR THE TRIP WAS TO BE 36600 LBS (INCLUDING 400 LBS FOR TAXI). THE FUELER STATED HE HAD THE PROPER GALS DELIVERED BUT THE GAUGE WAS NOT INDICATING WHAT IT SHOULD. MAINT WAS ADVISED AT THIS POINT; AND THE GAUGE WAS DEFERRED INOP. DURING CRUISE IT OCCURRED TO ME THAT THIS FUELING PROB MAY BE RELATED TO THE CTR TANK FLOAT SWITCH. FAA DIRECTIVES REQUIRED THAT THIS SWITCH BE DEACTIVATED UNTIL ELECTRICAL MODIFICATIONS WERE MADE; AND WITH A DEACTIVATED SWITCH; FUEL QUANTITY WAS TO BE LIMITED AS PER OUR COMPANY PROC. SINCE WE HAD A PLANNED QUANTITY IN EXCESS OF THE MAX ALLOWED WITH A DEACTIVATED SWITCH; I ASSUMED THAT WE WERE ON A MODIFIED ACFT. UPON INVESTIGATION; I REALIZED THAT A MODIFICATION COULD ONLY BE CONFIRMED BY NOTIFICATION IN OUR PAPERWORK THAT 1 OF 3 COA'S (CHANGE ORDER AUTHS) HAD BEEN ACCOMPLISHED. I COULD FIND NO EVIDENCE THAT ANY OF THESE COA'S HAD BEEN ACCOMPLISHED AND I NOW HAD THE UNEASY FEELING THAT WE SHOULD HAVE BEEN LIMITED TO 13000 LBS OF FUEL IN OUR CTR TANK (BECAUSE OF THE INOP GAUGE). UNDER THESE CIRCUMSTANCES; OUR TOTAL ACFT FUEL LOAD SHOULD HAVE BEEN NO MORE THAN 33800 LBS WITH AN INOP CTR TANK FUEL GAUGE; OR 35200 LBS WITH A NORMAL FUEL QUANTITY INDICATING SYS. THERE WERE SEVERAL LINKS BROKEN IN OUR CHAIN OF SAFETY. I FEEL AS THOUGH ON THESE UNMODIFIED ACFT; DISPATCHERS SHOULD KNOW THAT MAX FUEL IS 35200 LBS. I FEEL THAT OUR LOAD PLANNER SHOULD HAVE REALIZED THAT CTR TANK FUEL SHOULD BE LIMITED TO 14400 LBS. I ALSO FEEL THAT OUR COMPUTER SYS SHOULD HAVE FLAGGED THE FACT THAT THIS ACFT HAD THE FLOAT SWITCH DEACTIVATED AND SHOULD NOT HAVE PRINTED OUT A FUEL SHEET WITH A REQUESTED FUEL LOAD OF 15900 LBS IN THE CTR TANK.