The first step is to get alerts working because that way FormMail can tell you why something didn't work.
If you've set DEF_ALERT in formmail.php you can run this test:
If you don't receive an email, then you need to find out why PHP cannot send you emails from your server.
Yahoo, for example, requires that the sender be a valid Yahoo address. To do this you can set $FROM_USER to your email address.
If that doesn't work, then you can try the testmail scripts we've provided (you mentioned something called "test.php", but I don't know what you mean).
There's no sensible way to proceed until alerts are being sent to you.