Thanks much, dln. Very educational following up on your suggestions. I'll learn this stuff yet. However, the problem seems to be a Windows bug. According to a nice tip from "Some Guy" at http://us3.php.net/mail, Windows has a bug in php/mail, which required me to insert line 12 in the code below. After this "ini_set('sendmail_from', 'myself01@locahost');" line was inserted, everything seems to be working correctly. My client is receiving something very close to properly formatted mail.
For anyone else dealing with this, here is my corrected PHP code:
...
1. <?php
2. echo "<p>Thank you, <b>".$_POST["name"]."</b>, for your message!</p>";
3. echo "<p>Your e-mail address is: <b>".$_POST["email"]."</b>.</p>";
4. echo $_POST["message"]."</p>";
5. $msg = "Name: ".$_POST["name"]."\r\n";
6. $msg .= "E-Mail: ".$_POST["email"]."\r\n"; // NOTE: Change the "\r\n" to "\n" in a Linux machine.
7. $msg .= "Message: ".$_POST["message"]."\r\n";
8. $recipient = "myself02@localhost"; // This is the receiving email address for the website.
9. $subject = "Form Submission Results";
10. $mailheaders = "From: My Web Site <myself01@localhost> \n";
11. $mailheaders .= "Reply-To: ".$_POST["email"];
12. ini_set('sendmail_from', 'myself01@locahost');
13. mail($recipient, $subject, $msg, $mailheaders);
14. ?>
...