I'm curious if this problem was ever resolved.
I'm currently working on one with the same apparent problem. HDMI cable seated and the little fan spinning, but no light from the projector. I also know that this particular Ember has a tendency to freeze, and it takes a cooling off period before it can be started up again. Because of this I suspect an overheating problem of some sort.
Some time ago I know someone had a sizable resin spill with this Ember which reached what I understand to be the main pcb. The projector assembly was entirely clean (except for a little resin on the black plastic mirror shroud).
I've started carefully cleaning the affected board of resin. Haven't been able to test if that has cured the freezing issue yet, but in any case the projector unit doesn't seem to get the correct signals.
I apologize for the lengthy post and hope someone can provide me with some input to get this machine to work. Thanks!