My Apple Watch side buttons will work but screen will not at all

What makes you think the buttons work? Without the screen you can’t even tell if the watch is switched off!

I suggest trying to charge the watch about 1 hour, then see if you have any response. Try a Forced Reset by pressing and holding both the Digital Crown and the Side Button (together, at least 10 seconds) until the Apple logo appears, then release the buttons. If there is no display give it at least 30 seconds holding the buttons before you abandon hope.

If that doesn’t get a result use link Contact Support to arrange getting the watch checked by Apple, either a Genius Bar appointment or mail-in Service.

You may have a dead battery. Suggest you make an appointment with an Apple store Genius Bar....https://www.apple.com/retail/geniusbar/