The problem with your script is this line:
if (document.getElementsByName('BillEmail').value == null)
which in your case is always undefined, regardless of whether you enter a value.
This is because
document.getElementsByName will return a collection of HTML elements.
As you want to access the first element, change your code to:
if (document.getElementsByName('BillEmail').value == '')
and you'll be good to go.
Oh, and you'll have to do the same for BillPhone, too.