I had a very very very similar issue to this on my 525i. Recheck the fuses in the glovebox, I think it was Engine Control, 14/15 that had the tiniest of tiny breaks, an auto electrician missed it! I spotted it and that solved my issue immediately. I had same symptoms, all lights would work with ignition but not even a click, replaced the fuse and boom, started right up like there was never an issue.