Martin Logan works when not plugged in

I own Martin Logan SL3s. I have no experience with the Cinema TM. But looking at a picture I can see the pannel. I assume you have a single center channel speaker. There should be a noticeable difference when the speaker is plugged in. Have you tried listening with the other speakers turned off to see if you hear a difference? It is possible the pannel is blown but I would think more likely it might just be a fuse. Also make sure that the power cord is tight.

The power is needed to drive the woofers. The panels derive their power from the speaker cables. Same with my Summit. If you play something with a lower frequency than speech, you should notice a difference.

Send it for repairs, I had that happen to the one I owned years ago. Your panel went bad

The power is needed to drive the woofers. The panels derive their power from the speaker cables.

I'm pretty sure it's the exact opposite, at least it was on my Ascents from a few years ago.
AC power for the panels
Cone woofers don't need external power source

The Ascent does not have a powered sub like the Summit, which draws power for it. I realized the Cinema does not either.