After accepting their B737-300 with a center tank fuel gauge MEL'd as inoperative and empty; the flight crew became suspicious when the gauge showed 9;700 LBS during taxi for takeoff. The preemptively used takeoff performance data reflecting an additional 10;000 LBS and left the center tanks fuel pumps on. The entire flight was performed using fuel from a tank logged as empty.

Narrative

This aircraft had the center tank fuel gauge MEL'd inoperative (it read zero). The tank should have been empty per the MEL. The night before; the terminating Crew logged 4;800 LBS of fuel remaining. Our flight required a slant fuel load of 17;200 LBS. The Fueler added 12;500 LBS. The wing gauges indicated 9;200 LBS in the left and 8;400 LBS in the right. The center tank gauge (inoperable) showed 9;700 LBS. We verified the wing tank readings with dripsticks and disregarded the erroneous center gauge.During taxi; we considered the possibility of there being fuel in the center tank and turned on the center tank pumps. The low pressure lights went out immediately. During a short ground delay for a flow time; we recalculated our takeoff performance adding 10;000 LBS to our loadsheet weight. We were still well below any performance or structural limiting weight. We decided to just operate at the higher assumed weight. During the flight; we used only the 'empty' center tank fuel until on the downwind at our destination and we turned the pumps off with about 2;000 LBS indicated on the center gauge.After arriving at the gate; I went down to have the Fueler open the manual defueling valve so we could transfer the remaining center fuel into the wings. The transfer took about three minutes and the gauge read 400 LBS when empty. We dripsticked once more to confirm the wing fuel. To date; no fuel ticket has been found to explain the approximately 9;700 LBS in the center tank.