Sounds like a controller fail as Robyn said, or it's not getting power where it should. If the controller computer isn't happy, stop there. Definitely get it over to your tranny upfitter guy.

No problem towing a 4x4 in Neutral, as long as the Neutral we're talking about is the transfer case. NO tranny neutral towing though, for one mile or 8 (short of a dire emergency). Just get the transfer case in neutral.