iPhone touch screen not responding, iPhone will not force restart

I have a 2nd gen SE iPhone. The touch screen stopped responding earlier today, along with the fingerprint reader. I've been trying to restart my iPhone, but obviously can't slide the bar across to turn it off. I've also tried volume up, volume down, and holding the side button but nothing ever happens (eventually the phone screen just goes dark like a button isn't being held down). I've tried holding the side button and the home button, but no matter how long I hold that it just results in a screenshot being taken. I've tried holding the side button and volume buttons all down at the same time and nothing happens.

Any tips? I've got my phone plugged into my laptop, because I read somewhere that it might be helpful, but I can't unlock my phone to approve the connection to my laptop so it isn't even showing up in my finder.