I gave in and up and purchased an Nvidia Geforce GTS 250, simply because it was the only one in the city that had true HDMI out. And I only had 10 days left before I could return the HDMI cable for a refund if needed. It was $180, which makes me sad since I can get it a lot cheaper online, but all I care is that it works! Apparently the ATI Radeon HD 3200 integrated video was not powerful enough to sustain itself with this Pioneer TV. There have been a couple hiccups while I have been playing music for the last 7 hours, but I still have an image! And I have even shut off the TV, come back later, turned it on, and the HTPC was still showing on the TV! I have my fingers crossed that it will stay consistent! It just hiccuped again, where the sound cut out for 3 seconds and the image froze for about 1 second, but went back to playing music.
One major issue I had, that took me 3 hours to resolve today was trying to get the sound to work through HDMI. After trying EVERYTHING and searching Google, I thought... hmm... maybe there are updated audio drivers for the board that didn't come with the updated motherboard drivers... SURE ENOUGH with a simple 8 minute download and install I had sound!
To say the least, I did a little happy dance when I had video AND sound! Overall, it cost about $250 for the fix (I am keeping the $70 HDMI cable) and 4 months of battling this issue. Now that it is working, I am not risking changing a thing!