Ok, make sure that your hosting supports PHP and the file with the PHP code must be with extension .php (.html might also work, but usually not by default).
Why don't you try copying the code from this example of a PHP mail form
and see if you receive the email. Of course, you'll have to edit the email addresses.
The code from the top rectangle must be saved as file "mailform.php" and the other from the larger rectangle you can name whatever you want. It's crucial that both are in the same directory (folder) on your server.
When you upload them on your hosting, you need to access not mailform.php but the other file through your browser, fill out the fields, submit and see what happens.
If this works, then it means the connection with flash isn't working properly. If it doesn't, then it's most likely the php support on your hosting. Make sure that the email isn't caught by spam filters on your hosting.
p.s. I'll be on a long trip in the coming few days, so unfortunately I won't be able to provide you with more help for a while. If you find it difficult to understand the code and how things work, I suggest you find someone around you who has some experience to either help you or build the contact form for you.
• Some old Nikon SBs...