Hi,
If you believe the phone is still powering up (***and not overheating or smoking up, power it up without screen on to check***), you can try to connect to iTunes to see if you can do backup without the screen on.
If iTunes does see the phone you should be able to do a backup which you can use restore to on another phone.
Otherwise you’ll need to take it to a repair shop that does micro soldering to assess, identify and repair burnt components & possibly another screen, or to recover data for you.
Hope this helps