Saw this thread so I thought that I will share my experience with replacing keyboard in my x240 because I had problems with turning the machine back again. After the keyboard was replaced, I periodically tried to turn on the laptop to see whether it works or not. While I did not assemble it back completely (by that I mean putting the X240 into the covers) the laptop was working (turned on). When I plugged everything (wifi card, internal battery, etc.) and put machine into the case, then it wouldn't start upon pressing the power button. I was becoming desperate as to why the machine would work without covers and won't without them. After few tries I tried to start it without internal battery and it worked! But it must have been probably something else because when I let it run for a while, letting it charge the external battery from 0% to 100%, then I tried to disassemble one more time and plug in the internal battery as well. The machine started and charged the internal battery also from 0% to 100%. You have probably another problem but I thought that you might try to run it without battery like I did and maybe it will help.
Off-topic: I still have one problem with my X240 though, after successful replacement of keyboard the function (FN) key stopped working.
It's so annoying to adjust brightness, volume and everything using Windows.
W530 i7-3840QM (K2000M, 32GB RAM, WCG (Wide Color Gamut) FHD LCD (AUO B156HW01 V.4)) and one X230 i7-3520M (with Nitrocaster mod + FHD LGD IPS LP125WF2-SPB1) for travelling + PE4C (with Msi RTX 2060 SUPER Gaming X 8G in Pci-e slot).