Look for an inline fuse on the power line behind the unit on the console. Also check for loose power lines at the junction box.

Sounds like a typical new boat bug, look for the simple solutions first. Are you getting power to your control panel and not the fish finder or is the control panel dead as well?

As far as shutting the unit down with the boats power button, I have been doing that for years and have never had it cause a problem. I may be wrong doing it but so far it hasn't been an issue.

May want to post in the GPS and electronics forum.