Power button broken and can't switch on phone
I am not sure if this will really help you out or not but it is worth a try.
Make sure you have fastboot and USB driver for your phone is installed on your PC

Connect the a USB cable to your phone and keep on pressing the volume down button while the phone is booting.
If you are able to access the fastboot mode then you are saved and you can try fastboot reboot command.

If your phone is not entering into fastboot mode then go to a nearby shop and get the power button fixed. I think there is no other way you can turn on your phone.