Ok, I've had some luck. The TV is out of burn-in/aging mode, now I'm not exactly sure how I did it. So, for other people's benefit I'll explain what I had done.
Yesterday afternoon I finally found an old pair of computer speakers to hook up to my HTPC (running Windows 7 Ultimate 64-bit) to use as an interim solution until I could afford to replace the TV or we found a solution. My plan was to hide the small 2.1 setup behind the TV and in front of the tower. So, before moving the TV to do that, I had tested the TV to see if it had "fixed" itself and still no luck. So, I disconnected the TV, moved it, setup the speakers/connected them and routed all the wires. I then brought the TV back over and hooked it up. Then went to the sound manager in Windows and switched the playback device from HDMI to speakers. At this point, I tested the speakers and realized that I had positioned the satellites on the wrong sides (swapped left/right). Frustrated, I start unhooking the TV to move it so that I can correct my mistake. I unplug the HDMI cable and am expecting to see the now familiar and hated red/green/blue/black/white pattern but instead am greeted with a "no signal" message in a box. Suffice it to say I did a double take and then grabbed the remote and hit the menu button. Bingo! The menu came up! I powered the set on and off, still the no signal message! I changed the volume! Yay! I started doing a happy dance! I then went back into the service menu and looked at the menu with the burn-in mode, it was set to off. I then found the reset menu and reset the set to factory defaults. Once the TV had finished resetting itself, I reconnected the HDMI cable and set the playback device back to HDMI and tested it with a video and was greeted with sound! I then proceeded to unplug the TV and remove the speakers as I didn't need them back there anymore.
So, the only thing that I can think of that I had done differently was changing the audio playback device from HDMI to speakers. Maybe that was enough of a change on the input signal that it had kicked it out of the burn-in/aging mode? Either way, the TV is working again and I'm not going to screw around in the service menu again. Although, part of me wants to test it out to see if changing the playback device actually did fix the issue. But, I think I won't as I am afraid that I'll get it stuck in the burn-in mode again and not be able to get it out.
I just wanted to take the time to thank everyone for all their help and ideas/advice with this issue.