Have you tried contacting Outlaw Audio?
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"When I go to plug in a 1/8" cable to the trigger of the amp, the amp turns off. When I take the cable out, the amp switches back on."
Does the trigger work after you plug it in?
If not, take the batteries out of the remote and then try it.
This is just a complete guess, but maybe the trigger cable needs to be mono or stereo.
Try this, as I think the power switch has a mechanical "in" and "out" position. Simply with the amp main power switch in back turned to off, depress your front power button once. Then turn your power switch on again. Now hook up the trigger wire and try again.
I had a similar issue with a brand new 7125 and this fixed it.