A B737-500 IN CLB TO FL200 DIVERTED DUE TO LOSS OF NUMEROUS SYSTEMS; INCLUDING CABIN PRESSURIZATION. CAUSED BY ACFT SWITCHING FROM AIR MODE TO GND MODE TO AIR MODE CONTINUOUSLY.

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ON CLBOUT FROM ZZZ; I INITIALLY NOTICED TCAS FAIL LIGHT. SWITCHED TO OTHER XPONDER AND NO LUCK. FO BEGAN WORKING THE PROBLEM TO RESTORE XPONDER. AT LEVEL OFF; AUTOTHROTTLES WERE INOP WITH NO VISUAL/AURAL WARNING. ATC WAS ASKING VERIFICATION OF ALT AND POSITION. NEXT CAME A TURN TO INTERCEPT THE VICTOR AIRWAY ON COURSE. LNAV ALSO WAS NOT FUNCTIONING. HAD TO GO TO MANUAL NAVIGATION. SINCE FO IS NOT ISSUED LOW CHARTS; I PULLED OUT THE CHARTS AND DIALED APPROPRIATE NAVAID AND COURSE. ATC REQUESTED POSITION/ALT SEVERAL MORE TIMES. WE WERE VERY BUSY TRYING TO WORK THE SITUATION; NAVIGATE; AND COMMUNICATE WITH EACH OTHER AND ATC. ASSIGNED CLB TO 7000 FT THEN TO 12000 FT. IN CLOUDS; PRECIPITATION AND ICING. ASKED FOR HIGHER. TURNED ACFT CTL OVER TO FO. CHKED CABIN ALT; POINTED TO IT AND COMMENTED CABIN IS GOOD. AS WE LEVELED OFF AT FL200; WE HAD A CABIN ALT WARNING HORN. I DONNED MY OXYGEN MASK AND FO REQUESTED LOWER. CABIN ALT MAXED OUT AT 10300 FT. WE WERE ABOUT 100 MILES E OF ZZZ1 AND DECIDED TO LAND THERE AFTER TALKING TO DISPATCH AND MAINT. AT ABOUT 50 MILES OUT; I SIGNED OFF WITH MAINT AND DISPATCH TO CONCENTRATE ON THE APCH. WE NEVER RECEIVED THE AUTO FAIL LIGHT ON PRSZNT PANEL NOR OFF THE SCHEDULE DSCNT LIGHT. AFTER SWITCHING TO STBY; THE CABIN WAS CTLED FOR A BRIEF TIME AND THEN WENT UNCTLED BUT WE MAY HAVE CAUGHT THE CABIN SINCE WE WERE DSNDING THROUGH LOWER ALTS AT THAT TIME. LNDG AT ZZZ1 UNEVENTFUL.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE AIRPLANE WAS SWITCHING FROM AIR MODE TO GND MODE TO AIR MODE CONTINUOUSLY. XPONDERS; AUTOTHROTTLE INOP WITH NO WARNING. LNAV WAS NOT FUNCTIONING AND OPERATED ON MANUAL NAVIGATION. ON LEVELOFF AT FL200; HAD THE CABIN PRESSURE WARNING HORN. ACFT DSNDED TO A LOWER ALT AND DID CATCH THE CABIN USING MANUAL MODE. AFTER THE AIRPLANE WAS FIXED AT THE DIVERSION STATION BY COMPANY TECHNICIANS; THE AIRPLANE WAS FERRIED TO A COMPANY MAINT FACILITY. DURING THE FERRY FLT THE COMPANY TECHNICIANS EXPLAINED THE FAULTY GND AIR SENSORS AND TARGETS THAT FAILED ON THE R MAIN LNDG GEAR WERE IN BAD CONDITION AND THE WIRING WAS IN POOR SHAPE. THE RPTR INDICATED THE TECHNICIANS REVEALED THAT AT EVERY HVY CHK THAT WAS ACCOMPLISHED BY THE COMPANY MAINT; THESE SENSORS AND WIRING WERE REPLACED AND THE TARGETS WERE ADJUSTED. SINCE THESE CHKS HAVE BEEN FARMED OUT TO CONTRACT MAINT; THESE COMPONENTS ARE ONLY REPLACED IF DAMAGED OR ON TEST FAILURE.