A B737-300 ON TKOF CLB RETURNED TO THE FIELD DUE TO FAILURE OF THE CAPT'S ALTIMETER AND AIRSPD INDICATOR LINKED TO FAILED AIR DATA COMPUTER.

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FLT BEGAN FOR MY CREW AS A SCHEDULED ACFT SWAP IN ZZZ. INBOUND CREW RPTED NO PROBS WITH THE ACFT OTHER THAN AN EXISTING MEL FOR AUTO SPD BRAKE. ON ARR IN THE COCKPIT; I NOTED A 'COMPUTER' FLAG IN MY ATTITUDE INDICATOR AND A CURSER 'INOP' FLAG ON MY AIRSPD INDICATOR. THERE WAS ALSO A FD BOX IN THE HUD. NO OTHER INDICATION WAS APPARENT IN THE COCKPIT. ALL CIRCUIT BREAKERS WERE CHKED AND FOUND TO BE NORMAL. A CLICKING NOISE COULD BE HEARD IN THE MCP (AS WHEN A GUSTY WIND IS BLOWING THE FLT CTLS -- THIS WAS NOT HAPPENING). THE AIRSPD CURSER WAS FLUCTUATING BACK AND FORTH BETWEEN 215-180 KTS. DISPATCH AND MAINT CTL WERE CONTACTED AND CONTRACT MAINT WAS CALLED TO THE ACFT. SEVERAL CIRCUIT BREAKERS WERE CYCLED TO NO AVAIL. TECHNICIAN WENT TO THE E AND E BAY AND RE-RACKED SEVERAL COMPONENTS; STILL NO HELP. AFTER A LENGTHY DISCUSSION BETWEEN CONTRACT MAINT AND MAINT CTL; DECIDED THAT THERE WERE SOME FAILURES DUE TO AN FCC PROB. THE MECHANIC WROTE UP 5 SEPARATE SUBSYSTEMS: A AUTOPLT; SINGLE CHANNEL MACH TRIM; SINGLE CHANNEL SPD TRIM; ALT ALERTER; AND 'A' FLT DIRECTOR. UPON REVIEWING THE WRITE-UPS; I QUERIED THE STATEMENT 'DUE TO FCC FAILURE' AND I DIRECTLY ASKED MAINT CTL IF THERE WAS AN FCC FAILURE AND WAS TOLD THAT IT WAS NOT AN FCC FAILURE BUT A 'FAILURE OF A PORTION OF THE FCC' AND THAT THE ACFT WAS SAFE FOR FLT. IN DISCUSSION WITH DISPATCH; I RECOMMENDED THAT THE ACFT BE FERRIED THE SHORT DISTANCE TO ZZZ1 OR THAT MECHANICS BE DISPATCHED FROM ZZZ1 TO FIX IT. THE DISPATCHER WAS INSISTENT THAT THIS COULD NOT BE DONE. IN REVIEWING THE MEL; WE DETERMINED THAT WE WERE NON RVSM; CATI APCH LIMITED; NO 'A' AUTOPLT OR CAPT'S FD. I WAS SATISFIED AT THIS POINT THAT MAINT HAD ADEQUATELY TROUBLESHOT THE PROB AND THAT SINCE THE WX WAS GREAT ONCE WE GOT AROUND A BIT OF WX TO THE WEST OF ZZZ THE FLT WOULD BE NO PROB. DISPATCH SENT A NEW RELEASE AT FL280 AND THE FUEL ONBOARD WAS ADEQUATE. WE ELECTED TO DO A BLEEDS OFF TKOF SINCE MARGIN WAS 1100 FT AND TAXIED FOR TKOF ON RWY 12R NEARLY 2 HOURS AFTER DISCOVERY OF THE PROB. TKOF WT WAS 123000 LBS. WE WERE CLRED FOR TKOF AND THRUST LEVERS WERE ADVANCED. IT WAS THE FO'S TKOF. WE WERE A LITTLE SLOW SETTING TKOF THRUST; I QUICKLY GLANCED DOWN TO VISUALLY CLEAR THE RWY; AS IS MY HABIT; AND THEN CAME INSIDE TO MAKE THE 80 KT CALL. MY A/S INDICATOR WAS STILL ON ZERO; BUT WE WERE ROLLING PRETTY QUICKLY; A CROSS CHK OF MY STBY AND MY FO'S ASI SHOWED WE WERE ALREADY AT 90 KTS. I QUICKLY DECIDED THAT CONSIDERING THE CONDITIONS HVY WT; SLIGHT TAILWIND; 8500 FT RWY; SMALL STOPPING MARGIN; AND VMC WX THAT THE MOST PRUDENT COURSE WAS TO CONTINUE THE TKOF USING MY STBY INDICATOR. IT QUICKLY BECAME APPARENT THAT MY PRIMARY ALTIMETER WAS ALSO INOP (IT INDICATED CABIN ALT THE ENTIRE FLT). MY FO AND I QUICKLY DETERMINED THAT A RETURN TO THE ARPT WOULD BE NECESSARY AND AFTER CONFERRING WITH DISPATCH; DECIDED TO BURN DOWN FUEL WHILE REMAINING VMC AND TO LAND THE ACFT BACK AT ZZZ WHEN THE WT WAS REDUCED BELOW MAX STRUCTURAL LNDG WT. THE FMC WAS NOT PROVIDING COMPLETE OR ACCURATE INFO. FUEL CALCULATIONS WERE NOT PRESENT; NOR WERE N1 SETTINGS. WE DETERMINED LNDG WT BY ADDING FUEL GAUGES TO ZFW. LNDG WT WAS 113000 LBS. CAUSE: INCOMPLETE TROUBLESHOOTING AND NEVER REALLY DETERMINING THE EXTENT OF THE PROB. I BELIEVED THEM WHEN MAINT TOLD ME IT WAS ONLY A PARTIAL FAILURE. I SHOULD HAVE DETECTED THE ASI FAILURE SOONER. I WILL ADJUST MY PRIORITY TO CHK IT SOONER IN THE FUTURE. THERE WERE NOT MANY COCKPIT INDICATIONS OF THIS FAILURE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED ALL OF THE ACFT EQUIP PROBS WERE RELATED TO THE #1 AIR DATA COMPUTER AND INDICATED THAT IF THE SYSTEM WERE SELF TESTED PROPERLY; THE PROB COULD HAVE BEEN CORRECTED WITH A UNIT SENT TO THE STATION. THE RPTR INDICATED THAT FIVE DEFERRED ITEMS WAS TOO MANY ON ONE MAJOR SYSTEM AND THE AIRPLANE SHOULD HAVE BEEN TAKEN OUT OF SVC.