Just got an unresponsive #ThinkPad X240 to power on and boot again.
I took it apart and reset the internal battery cable, the memory module and held down the little reset button near the right hinge (also accessible through the case by an unmarked pin hole).
Put it all back together and it seems to be working fine now.
This is an issue that I've seen with a number of ThinkPad laptop models, but seems to be more common with the 12 inch X240 and X250.
If a #ThinkPad is competely unresponsive, no power indication or anything, put a bent paperclip in the pin hole on the bottom of the laptop and hold down the hidden reset button for about 25 seconds.
That often brings them back to life.