A B737-400 AFTER LEVELOFF AT FL260 DECLARED AN EMER AND DIVERTED DUE TO LNAV; #1 AND #2 XPONDERS; AND FMC 'VERIFY POS' MESSAGE; AS WELL AS NUMEROUS OTHER FAILURES. WHEN CABIN PRESSURE WARNING HORN SOUNDED; FLT CREW DECLARED EMER AND DIVERTED.

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ACCEPTED ACFT FROM THE INBOUND CREW. THEY WERE HAVING AUTOTHROTTLE PROBS; SO THE AUTOTHROTTLES WERE MEL'ED INOP. DEPARTED ZZZ1 ON DAY 3 OF FIRST OPERATING EXPERIENCE TRIP. I WAS PLT MONITORING AND THE CAPT WAS THE PF. AFTER TKOF LNAV WOULD NOT ENGAGE. ATC RPTED THAT OUR XPONDER WAS NOT WORKING. I SWITCHED TO #2 AND THAT DID NOT CORRECT THE PROB. VNAV WOULD NOT ENGAGE. FMC BEGAN DISPLAYING 'VERIFY POS' MESSAGES. FMC 'N1' PAGE DISPLAYED THE TKOF PWR SETTINGS RATHER THAN INFLT PWR SETTINGS. FMC TKOF PAGE DIDN'T CYCLE TO THE CLB PAGE. THE CAPT SAID THAT THE AIRPLANE STILL THINKS IT IS ON THE GND. WE BOTH CHKED FOR NORMAL CABIN PRESSURIZATION AND VERIFIED THAT THE CABIN WAS PRESSURIZING. THE CAPT HAD ME CHK ALL CIRCUIT BREAKERS SINCE WE COULD NOT A FIND A QRH ITEM THAT ADDRESSED OUR PARTICULAR PROB. NO TRIPPED CIRCUIT BREAKERS WERE FOUND. AMIDST NUMEROUS CALLS FROM ATC VERIFYING OUR POS AND ALT; WE CONTINUED OUR CLB TO FL260. SEVERAL MINS AFTER LEVELING OFF AND APPROX 30 MI N OF ZZZ VOR; THE CABIN ALT WARNING HORN SOUNDED. THE CAPT DECLARED AN EMER; AND WE ACCOMPLISHED AN EMER DSCNT WHILE DIVERTING TO ZZZ. DURING DSCNT; THE 'OFF SCHEDULED DSCNT' CAUTION LIGHT ILLUMINATED. WE HAD REACHED OUR PLANNED CRUISE ALT OF FL260. THIS LIGHT EXTINGUISHED SOME TIME PRIOR TO RECALL ON THE LNDG CHKLIST; AS NO LIGHTS SHOWED UP ON THE RECALL. THE CAPT PERFORMED A NORMAL LNDG. ON POSTFLT THE CAPT FOUND THE MACH TRIM CIRCUIT BREAKER WAS TRIPPED. THIS ALSO DID NOT SHOW UP ON RECALL DURING THE LNDG CHKLIST. AFTER LNDG IN ZZZ; IT WAS FOUND THAT THE MAINT PROC FOR THE AUTOTHROTTLE DEFERRAL HAD NOT BEEN COMPLETED PROPERLY; AS THE APPROPRIATE CIRCUIT BREAKERS WERE NOT PULLED. OUR FLT ENCOUNTERED MULTIPLE MALFUNCTIONS; NONE OF WHICH WERE ADDRESSED IN THE QRH. EITHER THIS OCCURRENCE NEEDS MORE EMPHASIS DURING TRAINING EVENTS OR A QRH ITEM SHOULD BE MADE TO AT LEAST ADDRESS THE AIR-GND SENSOR. THERE WAS PROBABLY NOTHING WE COULD HAVE DONE TO CORRECT THE PROBS WE WERE HAVING; BUT ARMED WITH THE PROPER INFO REGARDING THE STATE OF THE ACFT WE COULD HAVE MADE A MORE INFORMED DECISION ABOUT THE PROPER COURSE OF ACTION. I WOULD BE CURIOUS TO KNOW IF THIS HAS HAPPENED BEFORE TO OTHER CREWS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED BEING NEW TO THE AIRPLANE; THE FAILURES WERE COMING FAST AND FURIOUS AND CHKING THE CIRCUIT BREAKERS WAS ACCOMPLISHED IMMEDIATELY. ON THE GND AT THE DIVERSION STATION; MAINT DID NOT GIVE ANY DETAILS ON THE PLANNED MAINT ACTION.