the rental form requires the form querystring to load, that querystring needs to be included in the forms action so that when the form posts, it will post to the correct plugin page.
the forms action needs to pass the querysting, change:
<form class="Cool_Default" id="RentalInquiry_Cool_Default" name="RentalInquiry_Cool_Default" method="post" action="<?php echo $_SERVER["PHP_SELF"]; ?>">
to:
<form class="Cool_Default" id="RentalInquiry_Cool_Default" name="RentalInquiry_Cool_Default" method="post" action="<?php echo htmlentities($_SERVER["PHP_SELF"]); ?><?php echo (isset($_SERVER["QUERY_STRING"]) && $_SERVER["QUERY_STRING"] != "")?"?".htmlentities($_SERVER["QUERY_STRING"]):""; ?>">