I would suggest that the issue with the pop bumper sounds like a mechanical problem if you can hear it humming and moving slightly. Is anything bent or out of position causing the mechanism to bind? When it first refuses to fire can you move the pop bumper mechanism by hand?
If the gate still doesn't work after changing the driver transistor and pre - driver transistor then perhaps the problem lies further upstream with the 7408 (?) or PIA chip. Do you have the schematic and a DMM/logic probe?