Hi there, I'm sorry to hear you're having issues, but I'll help as best I can!
How did you test the cable between the 2 pedals? It's possible that the patch cable is working in some applications, but not others. Not all patch cables strictly adhere to the 1/4" spec, so it's possible it works in your test setup but does not work with the PolyTune output jack or the ParaEq MKII Deluxe input jack. Have you tried another cable or a cable from another brand?
Also, power. The ParaEq MKII Deluxe is true bypass by default, so even if it isn't powering on, your signal should pass through without issue. However, there is an advanced configuration option where you can set it in buffered bypass, so if you have that enabled and it isn't getting enough power (300mA 9Vdc center negative), it will not turn on, and in that case, your signal will not pass through.
Instructions for advanced configurations can be found in the manual. I can't speak for the PolyTune, but I assume it's buffered bypass.
Hope that helps!