The basic problem is that the process of submitting a form from a webpage requires sending an HTTP request to the 'action' URL for the form. This means that the current page unloads and the browser displays the response to its HTTP request, so, essentially, the second form on your page no longer 'exists'.
AJAX is a part of JavaScript, and is supported in all browsers. So 007Julien is correct that you could use it to submit the contents of the EMail form in the background (and not worry about the response), and then let the page process the submission of the PayPal form normally. It wouldn't be difficult, and if you search on "AJAX tutorial' I'm sure you could learn how to do it in a very short time. But there might be a better way all around.
Some PayPal shopping cart functions offer a callback notification that can be sent back to your website. That notification would show whether or not the user's payment was received, so you could have a script on your site that would send a message only if the payment went through properly. You might look into that. Good luck!