I have exactly the same problem in about 90% of the time when I power the kit. To isolate the problem, I used a breadboard instead of the pcb, used a different Wemos and tried some other sketches.
In my case, it's definitely the display. It's extremely sensitive in respect to (not soldered) wiring and small vibrations.
Correction: got me a new Wemos Mini Pro and now the kit works flawlessly.