Hi,
Without being able to reproduce the problem or without the error message ehind the problem, we can't provide a solution as we don't know the problem.
If you get a blank page during the checkout, it means that there is a fatal error during the process of a page.
So you should have the error message logged in the PHP error log of your web server.
You can also activate the "error reporting" setting of the Joomla configuration so that it would display the error message on the checkout.
Once you have the error message, provide it to us and we should be able to tell you what's going on.