I would start by re-installing the original cracked screen if it was still usable (at least for testing purposes). then see how the phone behaves.
Normally, a screen issue shouldn’t affect the power button but seeing as how you have a few issues and they correlate to your new screen, it’s the first thing to try.
Also closely inspect all of the flexes, connectors and surrounding areas for any sign of damage. Eyeballs may not suffice so use some form of magnification (magnifying glass, jeweller’s loupe or the zoom function on another phone’s camera).