Mid '14 MacBook air won't turn on

Big troubles in little China...

My 2014 MacBook air won't turn on. When I plug it in to the Magsafe, the LED lights up amber, as if it were charging - but I guess it's not.

The story is a little complex. My husband and I are cycling through China, and we're weeks from being in a city with an Apple store. We took the fast train to Hong Kong for the weekend a couple of weeks ago and I plugged in my computer to charge it. Later that weekend, when the battery had died, I plugged it in to charge and left it for a bit. That's when it started.... Or stopped starting as the case may be.

I took it to the Apple store in Hong Kong and they said it was probably the logic board. For time sake, we sent it to a friend in Beijing who took it to an authorized repair provider who turned it on without a problem, cleaned it out, charged for the diagnostic, and they sent it back.

I just got my computer back a few hours ago. Hit the power button to make sure it would turn on, it did, so I popped it on the charger and we went to dinner. When we got back, it wouldn't turn on again...and that's where we are. I've done all of the things Apple said to do, including resetting the SMC.

Thoughts? Questions? Advice?