I suppose there could be a problem with the HDMI port(s) on your TV, but I think it's more likely something to do with the way the two devices send/receive video signals, especially since you said the AppleTV works on your plasma.
I know this much:
When I plug a MDP cable into the back of my iMac, it does nothing until I connect the other end of the video cable into a video source/display. Also, my Samsung TV will not allow me to select an HDMI video source that is not active.
Seems odd that even after disconnecting your AppleTV from the same HDMI port that you switch over to your iMac, and the TV shows "check signal cable," that the TV would still not tell the computer to send its video signal. I wish I had the cable to test my Samsung out for you.
Most places that sell big TVs have pretty good return policies on them. If using it as a display for the iMac is a large part of what you want it for, it would probably be worth exchanging it for another TV.
Spike