A B737-400 EXPERIENCED A GND/AIR SENSE SWITCH FAILURE AND SUBSEQUENTLY RECEIVED MULTIPLE SYSTEMS MALFUNCTION INDICATIONS WITH A FAILURE TO PRESSURIZE. AN EMER WAS DECLARED.

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DEPARTED ZZZ1 ON DAY 3 OF OPERATIONAL EXPERIENCE FLT WITH A NEW HIRE FO. AUTOTHROTTLES WERE MEL'ED IN ZZZ1 DUE WRITE UP ON ACFT ARR. WHEN I SPOKE WITH MAINT CTL TO COMPLETE THE ENRTE MEL FOR THE AUTOTHROTTLES; I EXPRESSED MY CONCERN ABOUT THE WRITE-UP'S MENTION OF THE ACARS 'RESETTING' AND SENDING A FALSE ON TIME WHILE IN FLT. I SAID THAT I WAS CONCERNED ABOUT TWO UNRELATED SYSTEMS HAVING SIMULTANEOUS MALFUNCTIONS. HE RESPONDED WITH SOMETHING TO THE EFFECT THAT THERE WAS NOTHING HE COULD DO ABOUT THAT. ON DEP ZZZ1; LNAV MOMENTARILY ENGAGED; THEN DISCONNECTED. VNAV WOULD NOT ENGAGE. ATC RPTED OUR XPONDER NOT RECEIVED. TRIED SECOND XPONDER; ALSO NOT RECEIVED. FMC DISPLAYED 'VERIFY POSITION' MESSAGE. FMC 'N1' PAGE DISPLAYED THE TKOF POWER SETTINGS; NOT THE INFLT POWER SETTINGS. FMC TAKEOFF PAGE DID NOT CHANGE TO CLB PAGE. I COMMENTED TO THE FO THAT THE AIRPLANE STILL THINKS IT IS ON THE GND. FO CHKED FOR TRIPPED CB'S AND LOOKED FOR AN AIR/GND SENSING CHKLIST. PRESSURIZATION SHOWED NORMAL DIFFERENTIAL AND SLOWLY CLBING CABIN. CLBED TO FL260. SEVERAL MINUTES AFTER LEVELOFF; APPROX 30 MILES N OF ZZZ; CABIN ALT WARNING HORN SOUNDED. DECLARED EMER; ACCOMPANIED EMER DSCNT AND DIVERTED TO ZZZ. NORMAL LNDG. POST FLT FOUND MACH TRIM CB WAS TRIPPED. AFTER LNDG IN ZZZ A REVIEW OF MEL 22-4A SHOWED THAT THE MAINT PROC TO PULL THE AUTOTHROTTLE CB'S WAS NOT ACCOMPLISHED. I DID NOT CATCH THIS ON THE GND IN ZZZ1 AND MAINT CTL DID NOT DIRECT ME TO PULL THESE CIRCUIT BREAKERS. RECOMMENDATIONS: WE WERE FACED WITH MULTIPLE UNRELATED SYSTEM MALFUNCTIONS THAT; AS A GROUP; WE HAD NOT SEEN BEFORE AND THAT NO CHKLIST ADDRESSED. THE ONLY CHKLIST THAT ADDRESSES AIR/GND SENSING IS THE 'LNDG GEAR LEVER WILL NOT MOVE UP AFTER TKOF' CHKLIST. WE DID NOT HAVE ANY OF THE SYMPTOMS DESCRIBED IN THAT CHKLIST. I RECOMMENDED THAT AIR/GND SENSING FAILURES BE RESEARCHED AND THE RESULTS OF THE RESEARCH BE PROVIDED TO OUR CREWS THROUGH THE QRH OR TRAINING MATERIALS.