I have a NodeMCU Esp8266 v3 (Lolin) and it works fine conecting Vin and G to my cell phone power supply rated 5.1V, 1000mA. This develop board has a aprotective diode (the closest to Vin), if you have a Multimeter o multitester you can check it measurent contininuity, ifmeasurement continuity. If your diode is damaged the power applied to Vin never be enough to power up the nodemcu.
Regards from Mexico City.