THe very idea that you had NO audio AT ALL, then it worked, then it went back to NO audio AT ALL would imply to me the amp is not powered up.
I don't have the service manual in front of me, but I believe there is only one power lead and one ground going to the amp. Seems easy to verify with a multimeter.

I do not believe there is any 'enable' line on the amp for you to check, but you should verify that in the service manual. The fact your factory and Kenwood head are acting the same tells me the issue is the amp. IF you got a good amp, then the issue is power or enable to the amp. (Remember that "power" includes a good ground connection.)