Totally dumb suggestion -- have you tried hitting TIVO quickly when it was in the welcome video?
That may at least be a temporary workaround. I seem to remember having a similar problem on my Tivo HD drive that is apparently 'corrupted'. It works mostly, but gets 'confused' (stops recording things, etc.,) after a while. I was able to put it back in temporarily to get stuff off.. and I plan on doing that again.. But replacing it with another drive was better..
I know you already replaced your drive. I have no idea, but another *total guess* as a hail mary would be to try a clear & delete everything.