A B737-700 PLT DESCRIBES DEPARTING WITH THE AP 'STAB TRIM' SWITCH INADVERTENTLY 'OFF' PREVENTING RVSM OP.

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BOTTOM LINE WAS WE MISSED SOME SWITCH POSITIONS AFTER MAINT WAS DONE ON ACFT. THIS WAS THE CULMINATION OF AN EXTENDED MAINT DELAY AND LONG SIT TIME. ALTHOUGH WE WERE NOT FATIGUED WE WERE DEFINITELY TIRED. DUTY START: XD:22. I HAD AWAKENED THAT DAY AT XA:00. LANDED IN ZZZ1 AT XF:30. ACFT CHANGE AND SCHEDULED TO DEPART AT XI:00. OUR ACFT ARRIVED WITH A 'DISPLAY SOURCE' WARNING ON BOTH PLTS OUTER DISPLAY UNIT. EXTENDED GND TIME AWAITING PART. FINALLY PUSHED BACK AROUND XN:00. AFTER ENGINE START HAD 'MASTER CAUTION' AND 'ENG' ANNUNCIATOR ILLUMINATE. NOTED THAT BOTH NUMBER ONE AND TWO ENGINE ELECTRONIC ENG CONTROLS WERE IN 'ALTN' MODE. SHOULD HAVE JUST SELECTED 'ON' FOR BOTH ELECTRONIC ENG CONTROLS BUT INTERPRETED THIS AS A MALFUNCTION. THIS THE RESULT OF THE PREVIOUS DISPLAY ELECTRONIC UNIT MALFUNCTION AND MAINT WORK. WE DEPARTED WITH AN ENROUTE MEL UNNECESSARILY. AFTER TAKEOFF 'MASTER CAUTION' AND 'FLT CONT' ANNUNCIATOR ILLUMINATED. NOTED AMBER 'SPEED TRIM FAILURE' WARNING LIGHT ON OVERHEAD FLIGHT CONTROL PANEL ILLUMINATED. COMPLETED DEP AND AFTER T/O CHECK AND SPEED TRIM FAILURE CHECKLIST IN QRH. THEN NOTED THAT AUTOPILOT(S) WOULD NOT ENGAGE. REALIZED THAT WE WERE NO LONGER RVSM EQUIPPED AND STOPPED CLIMB AT FL280. FORTY FIVE MINUTES AFTER TAKEOFF NOTED THAT AUTOPILOT 'STAB TRIM' CUTOUT SWITCH WAS 'OFF.' RESET SWITCH; RESTORED AUTOPILOT AND RESUMED RVSM OPS. MADE THE CORRELATION THAT THIS WAS ALSO THE CAUSE OF THE SPEED TRIM FAILURE. DARK FLIGHT DECK AND STAB TRIM CUTOUT SWITCH PANEL IS NOT BACKLIT. SWITCHES APPEARED IN NORMAL POSITION AND COULD NOT SEE RED BAND IN THE DARK. LESSON LEARNED: DON'T JUST LOOK; PHYSICALLY TOUCH SWITCH AND GUARD IN RIGHT POSITION. PERHAPS ADD A STEP TO 'SPEED TRIM FAILURE CHECKLIST' TO INCLUDE CHECK OF STAB TRIM A/P CUTOUT SWITCH.