Help needed with PHP form

Hi, I’m trying to get my order form to work with php to send information to the email I specify. I got the tutorial from this site and I’m doing everything it says to make it work, but obviously something is wrong. Every time I go to submit the information I get my error message saying the data did not send. Could somebody please take a look at my code and point me in the right direction? Thanks in advance. I’m new to coding like this, I’m a designer and I usually just stick to html and CSS.

Here is my html code:

<form  method="POST" action="mailer.php">
        <h4>Step 1 &#8211; Choose Wood finish</h4>
                  <input name="check[]" type="checkbox" value="natural_cherry" />
                  Natural Cherry <br />
                  <input name="check[]" type="checkbox" value="dark_cherry" />
                  Dark Cherry <br />
                  <input name="check[]" type="checkbox" value="custom" />
                  Custom 
                  <input type="text" size="30" maxlength="40" name="custominput" /> 
                  <br />
        <h4>Step 2 &#8211; Choose Top Type</h4>
       
                  <input name="check[]" type="checkbox" value="type0top" />
                  Type 0 Top <br />
                  <input name="check[]" type="checkbox" value="type1topleft" />
                  Type 1 Top Laptop Tray Left<br />
                  <input name="check[]" type="checkbox" value="type1topright" />
                  Type 1 Top Laptop Tray Right<br />
                  <input name="check[]" type="checkbox" value="type2top" />
                  Type 2 Top 
                  <br />
        <h4>Step 3 &#8211; Choose Desk Style</h4>
        
                  <input name="check[]" type="checkbox" value="ART_series" />
                  ART Series Desk<br />
                  <input name="check[]" type="checkbox" value="TEC_series" />
                  TEC Series Desk
                  <br />
        <h4>Step 4 &#8211; Choose Functional Desk Accessories</h4>
        
                  <input name="check[]" type="checkbox" value="computer_shelf" />
                  Computer Shelf (standard desk comes with 1 computer shelf) <br />
                  <input name="check[]" type="checkbox" value="printer_shelf" />
                  Printer Shelf<br />
                  <input name="check[]" type="checkbox" value="return_desk" />
                  Return Desk <br />
                  <input name="check[]" type="checkbox" value="desk_file_cabinet" />
                  Desk File Cabinet
             <br />
        <h4>Step 5 &#8211; Choose Office Accessories</h4>
        
                  <input name="check[]" type="checkbox" value="hutch" />
                  Hutch <br />
                  <input name="check[]" type="checkbox" value="book_case" />
                  Book Case <br />
                  <input name="check[]" type="checkbox" value="conference_table" />
                  Conference Table <br />
                  <input name="check[]" type="checkbox" value="desk_file_cabinet" />
                  Desk File Cabinet <br />
                  <input name="check[]" type="checkbox" value="meeting_table" />
                  Meeting Table
                  <br />
        <hr />
          <h4>Contact Information</h4>
          <p>
            <span2>* All fields required</span2>
          </p>
          <br />
           <label>Full Name: <span2>*</span2></label><br /><input type="text" size="30" maxlength="40" name="name" />
           <br />
                  <label>Address: <span2>*</span2></label><br />
                  <input type="text" size="30" maxlength="40" name="address" />
                <br />
                <label>Phone: <span2>*</span2></label><br />
                <input type="text" size="30" maxlength="40" name="phone" />
               <br />
                <label>Email: <span2>*</span2></label><br />
                <input type="text" size="30" maxlength="40" name="email" />
              <br />
                <label>Message: <span2>*</span2></label><br />
                <textarea rows="6" cols="25" maxlength="1000" name="message"></textarea>
                <br /><input width="50px" type="submit" value="Submit" id="submit_btn" name="" />
          </form>

and my php code:

<?php
if(isset($_POST['submit'])) {

    $to = "myemail@email.com"; 
    $subject = "Form Tutorial";
    $name_field = $_POST['name'];
    $address_field = $_POST['address'];
    $phone_field = $_POST['phone'];
    $email_field = $_POST['email'];
    $message = $_POST['message'];
    
    

    foreach($_POST['check'] as $value) {
        $check_msg .= "Checked: $value
";
    }
    
    $body = "From: $name_field
 Address: $address_field
 Phone: $phone_field
 E-Mail: $email_field
 $check_msg Message:
 $message
";

    echo "Data has been submitted to $to!";
    mail($to, $subject, $body);
    
} else {
    echo "Error, data did not send";
}
?>