I have a 2001 740i with similar issues. The radio works, then the Nav screen goes to a thin "static" line (nothing else) and the radio goes off. The radio will come on if I push the on/off button twice, but will stay on for only 2 mins or so.
I have found that I can pull the fuse on the right-hand side of the trunk (which is not burned out) and replace it, and the whole system will work normally. But, only for a few days.
I would love to know what is going on with this. I don't think the main components are broken, because as I said, they work normally upon the pull/replace routine with the fuse.
Any thoughts out there?