When I try to launch a game, my Monitor displays "No Support"

Hi all!

Ok lets get too my problem, I had just installed a new components in my case:

Motherboard: Biostar A780L3B
Processor: AMD Sempron
Memory: Kingston DDR3 2GB

I had an old Monitor that have been giving me Backlight problems installed on the computer up to a few hours ago because it started giving trouble again, so I hooked backup my 24" 1080p LCD HDTV back to my computer (I was using it as my monitor while I had my other monitor disconnected, long story).

Anyways, I was just trying to launch a game, the shield and what not for the game had loaded and the part where the game's loading screen was suppose to pop up, my monitor's screen when black and started displaying "Not Support".

So my question is, is it because my processor is only Single Core and doesn't have the power to display the game full screen on my TV? Or could it be something else? Because the computer displayed everything fine on my old monitor.

Also, I had planned to replace the Single core with a Dual Core or something, so should I just go ahead and do that?

Thanks in advance!