A B737-200 IMMEDIATELY AFTER TKOF DIVERTED DUE TO LOW PWR #1 ENG CAUSED BY A PART PWR TRIM ADJUSTMENT CREW DID NOT SECURE.

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ON THE NIGHT OF NOV/WED/00; I WAS ASSIGNED ACFT XYZ. THE ACFT HAD A PRIORITY ONE ITEM ASSIGNED REQUIRING THE ENG TO BE TRIMMED USING A PT7 GAUGE. AN ENG TRIM IS A JOB I HAD NO EXPERIENCE PERFORMING. DUE TO THE WORKLOAD AT OUR STATION 2 MECHS FROM XXX WERE SENT TO ASSIST ZZZ. WHEN THE 2 MECHS ARRIVED THEY WERE ASSIGNED TO HELP PERFORM THE ENG TRIM RUN ON ACFT XYZ. NEITHER OF THE 2 MECHS FROM XXX HAD EXPERIENCE PERFORMING AN ENG TRIM RUN. IN ESSENCE; THE 3 OF US WERE ATTEMPTING TO LEARN AS WE WENT ALONG. THE MAINT MANUAL WAS NOT CLR ON HOW TO HOOK UP THE TRIM KIT TO THE #1 ENG; SO WE WERE CONSTANTLY STOPPING AND HAVING TO ASK THE LEAD MECH FOR ASSISTANCE. THE LEAD WOULD STOP WORK ON ONE ACFT TO COME HELP US WITH ACFT XYZ. THE LEAD WAS INTERRUPTED FROM HIS WORK NUMEROUS TIMES DUE TO OUR NEEDING HELP. AFTER THE TRIM KIT WAS INSTALLED THE ACFT WAS TAXIED OUT TO THE RUN-UP AREA. WE HAD TO RUN THE TRIM TEST TWICE. AFTER RETURNING TO THE GATE ONE OF THE OTHER MECHS NOTICED AN AIR LEAK WHICH MAY HAVE POSSIBLY GIVEN US FALSE READINGS ON THE PT7 GAUGE DURING THE FIRST TRIM RUN. THE SECOND TRIM CHK THE LEAD RAN THE FLT CTLS WHILE I DOCUMENTED THE PERFORMANCE NUMBERS ON THE TRIM WORK CARD. I ALSO RELAYED THE READINGS FROM THE PT7 GAUGE TO THE LEAD; AS THE LEAD COULD NOT OPERATE THE ENG THROTTLES AND FACE BACKWARD INTO THE CABIN TO SEE THE THIRD MECH. ONCE ALL THE NECESSARY INFO WAS GATHERED WE RETURNED TO THE GATE. IMMEDIATELY UPON OUR RETURNING TO THE GATE THE LEAD WAS CALLED OVER TO ANOTHER ACFT. THE 2 MECHS FROM XXX QUICKLY DISCONNECTED THE TRIM KIT FROM THE ACFT AND RETURNED TO XXX. WHEN IT CAME TIME TO CLOSE THE ENG COWLINGS I AGAIN HAD TO HAVE THE LEAD STOP HIS WORK ON ONE ACFT TO ASSIST ME. AFTER CLOSING THE ENG COWLINGS THE LEAD AND I COMPLETED ALL THE PAPERWORK AND MADE THE NECESSARY LOGBOOK ENTRIES. THE ACFT WAS SCHEDULED TO DEPART IN APPROX 10 MINS. THE LEAD AND I COMPLETED ALL NECESSARY PAPERWORK VERY QUICKLY IN ORDER TO AVOID DELAYING THE FLT'S DEP. THE ACFT FLEW FROM ZZZ-ABC WITHOUT ANY MECHANICAL PROBS. OUT OF ABC THE CAPT DIVERTED THE ACFT DUE TO THE #1 ENG NOT MAKING PWR.