TWO LINE MECHANICS WORKING A B737-400 ACFT; EXPLAIN HOW MULTIPLE TASKS; DISTRACTIONS AND INTERRUPTIONS OF JOB ASSIGNMENTS LED TO THE DEPLOYMENT OF THE LEADING EDGE FLAPS THAT DAMAGED THE #1 ENG INBOARD THRUST REVERSER.

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I WAS ASSIGNED TO WORK ACFT X WITH A SVC CHK ATTACHED TO IT. INCLUDING IN THE WORK PACKAGE WAS AN INSPECTION ON #1 MAIN LNDG GEAR BRAKE. MEL ON THE #1 ENG R IGNITER; MEL ON #1 ENG GENERATOR INOP. OPS CHK FOR VOICE RECORDER; STANDBY PWR; INTERIOR EMER LIGHTS; CATIII HGS 30 DAY. WE ALSO HAVE AN ACARS REGARDING PRESSURIZATION ISSUE. WHEN THE ACFT ARRIVED WE MET IT TO HAVE A DETAILED TURNOVER FROM THE INBOUND FLT CREW REGARDING THE PRESSURIZATION ISSUE. WHEN THE ACFT WAS CLR OF PAX AND CARGO WE STARTED TO TROUBLESHOOT THE GENERATOR MEL ALONG WITH IGNITER MEL; BY ENG RUN IDLE. WE WERE ADVISED TO STOP WORKING ON THE MEL'S AND WE THEN STARTED TO WORK ON THE BRAKE CHANGE AS WELL AS THE #2 MAIN LNDG GEAR TIRE CHANGE. ENG STOP LINE SUPPORT CAME BY TO ACCOMPLISH THE IGNITER LEAD CHANGE WHILE WE WERE WORKING ON THE BRAKE AND TIRE. DURING THE CONFUSION OF WORKING MULTIPLE TASKS AND MULTIPLE PEOPLE WORKING ON THE ACFT; THE DEACTIVATION OF THE LEADING EDGES WAS NOT ACCOMPLISHED. WHEN WE WERE DONE WE WENT IN THE SHOP TO CLEAN UP. ON THE WAY BACK TO THE ACFT WE WERE INFORMED THAT THE LEADING EDGE FLAPS WERE DEPLOYED AND DAMAGED THE INBOARD THRUST REVERSER OF #1 ENG.