Are you still getting to the checkout failure page? If so then I think your local checkout if failing. To see what may be going on you will need to add the full request and full response bindings to your checkout failure page.
In this page select the part of the page that tells you the order failed, then go into split view add this into the code:
Linkpoint full request: <?php echo(LinkPointAPI_Result("Full Request")) ?><br/>Linkpoint full response: <?php echo(LinkPointAPI_Result("Full Response")) ?>
Then save and upload this page to the server and test it again. You might be able to test locally but the URLs will not work out correctly this way so it is best to test on a live server. This should let you know why the transaction is not being processed.