I have the TV hooked up to the PC using a Dynex HDMI Cable that I purchased at Best Buy. The Dell monitor is hooked up to the PC using a standard VGA Cable.
My problem is that the quality on the TV with the HDMI Cable is very poor. I went through and checked all of the resolutions and 1280 x 720 was the best, but it isn't great. The image is a bit fuzzy, and text is hard to read. The quality I had with the VGA Cable was much better.
I'm not sure what I can do to get a better picture. Any help would be great!
That model TV is really 1366x768 native instead of 1280x720. That might be tricky to get working on the HDMI cable, but should work with the VGA cable. Also, you might look at this page on the TV once you get the proper native resolution: http://www.lagom.nl/lcd-test/subpixel.php
This one might help you confirm that you're really at native resolution: http://www.lagom.nl/lcd-test/clock_phase.php
If the TV has a BGR layout or one of the vertical layouts, and you've got windows set to use RGB subpixel layout, that will make the text look bad.
I doubt it's the cable. Could be that the video card doesn't support 1366x768 properly over hdmi. You might try fiddling with the tv's scaling settings and with the overscan/underscan settings in Catalyst Control Center to see if you can get native (which will make it look like an even gray, rather than lighter gray squares over a dark gray background).