This HDTV can still impress with stunning images (depending on the source)...months later.
Since we are in a similar situation - early adopter and main board swap. I believe you nailed the power issue's source.
I also noticed that pressing the Netflix or Amazon icons on the remote's More view - without the network sends the F7100's CPU into a fit.
The result can be a shut off or cycle, also triggered by the STB tools channel guide's loading errors and other glitches.
I have seen the two Web Browser Apps before.....
My conclusion is that all the major issues from the dancing squares to power cycles have been software glitches.
The HDTV is just too complex and varied in its functions to offer a seamless experience.