Can I assume you left out the code to connect to the database? Otherwise, where does $dbh get set? If that's not set, just comment out your database code and see if you can get the ajax code working without it.
There's no script reference to jquery here. Recommend pressing F12 in Chrome or Firefox to see any javascript errors.
This:
$('#comment_form').keypress(function(event){
Should be:
$('#post_comment').keypress(function(event){
This:
data : {user_comm : comment},
Either do this above the ajax call:
let comment = $(this).val();
or this in the ajax call:
data: {user_comm : $(this).val()},
Lastly, I don't think you want this:
document.getElementById("display-comment").innerHTML = response +
document.getElementById("display-comment").innerHTML;
It will end up duplicating even the text area. Consider revising. You'll know better once you get something coming back.