HDMI display support for monitor...

I apologize in advance, I saw the iOS board, but it looked like that was strictly for mobile gaming so I came here.

My wife and I recently bought a MacMini.  I'm really enjoying it, but perhaps some tech folks out here could answer this question for me.

I'm currently using an older Sony TV through HDMI as a display, which works fine, but it's too big.  I also have an older (maybe 7 years old?) "Element" tv with an HDMI port.  When I use the Element through HDMI, I'm consistently getting no display to the Mini.  However, if I'm on my AppleTV using airplay, I can get a mirrored image back to the Element tv no problem.  I check in the display settings and it looks like it recognizes the Element...BUT, once I disconnect the AppleTV, the display to the Element vanishes and goes back to saying no signal.

Can anyone figure this one out?  Too be honest, I'd rather use this older tv since we had the Sony in our front room.  For the time being it does the job, but it's not a long term fix.

Appreciate the help in advance!  Thanks!

Still digging around trying to fix this...
 
So, I connect the Mini to the Sony tv.  It displays fine.  I then mirror it to my apple tv.  I then disconnect the Sony TV and connect the Element TV.  I'm getting a display no problem.  It works great.
 
However, as soon as I disconnect the airplay, the Element tv drops the display and states "NOT SUPPORTED."
 
I've gone through each resolution, and no dice.  My next step is to buy a VGA to HDMI adaptor and try that using the VGA port on the Element tv.

What is the model of your Mac Mini and Element TV?

I don't really know anything about Mac Minis, but I sometimes have issues switching my PS3 between TVs and the issue always ends up being the resolution it's set at.  Are both TVs the same resolution?  If the element is 720P and the Sony is 1080P or something then the Mac Mini might be set to output at too high of a resolution so you might have to lower the resolution while it is hooked up to the Sony and then try it on the Element.  That's just something I'm throwing out there as a possibility.  Hope you get it fixed.