My 6-year-old Panasonic plasma seemed impervious to anything. It's more or less impossible to burn in a plasma, by the way. I suppose you could do it with a music app if you really tried. That said, I doubt the app actually leaves a static image on the screen for hours, that would surprise me a great deal.
Let's say you have 10,000 hours on your plasma so it has about 50,000 good hours left. (These estimates are conservative.) About 10% of your initial brightness is gone by now and you have 40% left till "half brightness". Over 5,000 hours of Pandora -- assuming the image is static, which, again, seems unlikely -- you'll use up 1/10th of what's left or 4% of the total brightness of the screen. So you'd now need to detect a 4% brightness gap between the Pandora menus and the rest of screen. On solid backgrounds, that's a maybe. On regular content, that's a "no chance". And to even achieve that, you needed 10,000 hours of Pandora and "only" 50,000 good hours left.
There is no difference in HDMI cables. If you can see the picture without visible dropouts or sparklies, the cable is working at 100%. No other cable will display a better version of that picture. You're simply wrong if you think there is a better digital cable than one that is already working.