Di2 left shifter not working
I've heard of loose connections between the shifters and their cables causing this sort of issue. In one case in particular, the connector didn't latch properly and the bar tape pulled it out, so it would seem OK when tested but not when riding. 

In general if you've got battery and part of the system works, the connections are one of the first things to check - the front derailleur connector as well as the shifter connector. Here the lack of an LED on the controller suggests the shifter cable is at fault.