The HTML seems correct, as Price dropdown contains the right cat ID.
I guess this is a JS problem, my first guess is that you shouldn’t use the same variable name in both scripts.
Replace dropdown by dropdown_price for second one, like :
<!--DROPDOWN SORT CATEGORY 2-->
<script type="text/javascript">
var dropdown_price = document.getElementById("cat2");
function onCatPriceChange() {
if ( dropdown_price.options[dropdown_price.selectedIndex].value > 0 ) {
location.href = "https://wordpress.stackexchange.com/questions/124116/<?php echo get_option("home'); ?>/?cat="+dropdown_price.options[dropdown_price.selectedIndex].value;
}
}
dropdown_price.onchange = onCatPriceChange;
Let us know !