Just to review what the lights mean for every one -
Power Indicator light: Off = System is Off Blue = System is On Amber Flashing = S3 state
Battery Indicator light: Amber Flashing = Battery Low Amber = Charging Blue = Battery is charging
First unplug the charger and then disconnect the battery, as in Step 5, plugin the charger and see if it starts. If it does the battery may be defective.
Acer Spin 3 SP315-51-757C Battery Replacement
Before reconnecting the battery, while you are there disconnect the CMOS battery by disconnecting the black/red wire connector, almost directly below the fan in the below Repair Guide, and press and hold the power button for 30 seconds. If you have a multimeter test the CMOS battery for 3 volts:
Acer Spin 3 SP315-51-757C Motherboard Replacement
Just plugging in the charger see if it starts up. If yes then unplug charger and reconnect the battery. Does it start up?