A B757-200 ACFT EXPERIENCED SLOW STAB TRIM RESPONSE AND STAB TRIM LIGHT ON. ACFT ALSO TOOK HUGE DIP AND RIGHT WING DOWN AND BUMP WHEN TRYING TO ENGAGE CENTER AUTOPILOT.

Narrative

WE WERE DISPATCHED WITH 1 PACK INOP. AFTER STARTING ENGS AND PUSHING BACK FROM THE GATE; ZZZ INFORMED US OF 20-30 MIN DELAYS. WE SHUT THE R ENG DOWN. WHEN WE ATTEMPTED TO RESTART IT OUT POPPED THE R ENG CTL CIRCUIT BREAKER TWICE. TALKED TO MAINT CTL WHO SENT US BACK TO THE GATE. MAINT WORKED ON IT AND OFF WE WENT. THIS TIME WE KEPT ENGS RUNNING THROUGH DELAYS. DURING TKOF AND SHORTLY AFTER LIFT-OFF AIRPLANE FELT ODD. I ATTRIBUTED IT TO WINDS. THEN THE STABILIZER TRIM LIGHT CAME ON. IT WAS CLRLY TRIMMING VERY SLOWLY. I CONSIDERED RETURNING TO ZZZ BUT ACFT WAS FLYING AND WX BETTER TO THE W. ALL HYD SYS INDICATIONS WERE NORMAL. TRIED TO ENGAGE CTR AUTOPLT AND THE AIRPLANE TOOK A HUGE DIP; R WING DOWN; AND A BUMP AS IT FOUGHT PITCH CTLR. GAVE UP ON THAT AND HAND FLEW. FO FLEW WITH L AUTOPLT ON WHILE I RAN CHKLISTS AND TALKED TO DISPATCH AND MAINT CTL. THEY RECOMMENDED A PRECAUTIONARY LNDG IN ZZZ1 WHICH WE DID. WE DID NOT DECLARE AN EMER. WE DID REQUEST A SHALLOW STRAIGHT IN APCH TO RWY AND LESS THAN STANDARD TURNS TO AVOID THE POSSIBLE 'DIP' OF A WING. ALL WENT WELL ALTHOUGH I COULD FEEL THE AIRPLANE TRIMMING SLOWLY. STABILIZER TRIM LIGHT REAPPEARED. TOOK THE PEOPLE TO ZZZ2 IN ANOTHER AIRPLANE. THEY WERE IN GOOD SPIRITS AND APPRECIATED BEING KEPT IN THE LOOP. AN EXCELLENT JOB BY FO AND FLT ATTENDANTS.