Make backups first.... as always
Open register.tpl and at the top before all the code insert
Code:
{if $login eq ""}
You have to be a member to access this page (or you can redirect to login page or contact us page...)
{else}
and at the very bottom of the file insert
This will show "You have to be a member to access this page" to anyone who is not logged in and tries to access register.php. Make sure this also works with your checkout