Since your second monitor is a TV, I'm guessing it doesn't send the right EDID to the computer. You didn't say which version of Windows you were using.

I think probably what you need to do is create a custom INF file for the monitor/TV (or possibly just plug the appropriate values into the registry manually). You might also have to force the OS to use it. (I think the latter one might contain all of the information in the prior one.)