If your gauges are LCD, I would check the fuses, certainly. It would be entirely possible that the entire dashboard circuit is protected by a single fuse.
I would like you to check if the turn signals are working when you activate them, even if the display does not light. With the car running, check to see if each and all of the turn signals are working even if the dashboard tells you nothing is happening. If they are working but your dashboard doesn't report that they are working, and if the fuses are all okay, then there is a design flaw going on. Maybe there is a BMW expert with some experience with this, if not on this site, but online.