If you unplug the new home button and use a known good home button you can get the phone to power back on by unplugging the battery for a few seconds, plugging back up and use the home and power button together to get the screen on.
The issue is probably the replacement home button.
Sometimes when a home button is replaced it short circuits the phone. This doesn’t usually cause any further damage to the phone. The phone turns off and then won’t power on.
You need to get a new home button. Before you plug in the new home button ensure that the phone is on, and the screen is operating. Once you plug in the home button it will work.