Well, you are prophetic! I had turned the car on/off multiple times, but then gave up and came in to Google the problem. Found a multi-page thread of BMW owners (but non-i3) reporting this problem, dating back to 2013. No actual answers. For some, their dealers updated SW and flashed code, but problem would come back. Some dealers replaced the CIC (not sure what that is) but problem came back. Some dealers replaced the head unit but those people didn't report back to say whether or not the problem returned.
In any case, after Googling for 20 minutes or so, I went back out and turned the car on, and the screen lit up. So, I guess we'll see if this happens again or whether it was a fluke. This is the first time I've seen it in my almost 2 months ownership of the car. I just sent an email to the previous owner to see if he had ever experienced it, but haven't heard back yet.