Consider breaking it into bite-size testable pieces.
1 - check the return data from database. Is it what you want
2 - are you requesting the data correctly (i.e, can you just ECHO it?)
3 - Try to force-feed simple data into your dropdown - no SQL. Does it show?
If 1, 2, and 3 are work as expected, then you sort of narrowed your problem down to how you transform your SQL into text strings for display in the dropdown.
Simplify - when it works, then add other features until it stops working. Fix hose features.
Also, the value for a select is based on the select list - does not belong as attribute
<select name="id" value="">
<?php
DisplayRows();
?>