Inserting data into a WordPress table on form submit, using PHP

This is not the WordPress way. There's several issues, but let's start high-level.

Note: This answer assumes that you are working on the front-end, not on the dasboard.

First, your form tag should NOT point to a specific file. You should modify your form to point back to the page it is on. The lazy (not ideal) way to do this is to leave the "action" of the form tag empty. This will cause the form to post back to the same page / url it is displayed on:

<form method="post" action="">

Then, find your theme functions.php file, or your plugin main file, and "include" the insertrow.php file:

require_once "insertrow.php;

Then, you need to change your "watch" a bit so that it's a FAR more unique value than "submit". Since your form contains a select with the name of ticket_priority, I would suggest watching for that:

if(isset($_POST['ticket_priority']))
{
insert_row();
}

And, if you do this the way I'm suggesting, you won't have to include the WP code

// Comment the below line out.  Not necessary.
// require_once('../../../wp-config.php');

Lastly - on a WP site, you want to take advantage of the WordPress security tools that are in place. Using a NONCE input is a bare minimum to help ensure that the form was legitimately posted, rather than being spammed in. Check out wp_nonce_field and wp_verify_nonce.

Done more inline with the "WordPress way", your code would look something like so:

function display_form(){
    echo '
    <form action="" method="post">';
    // Add a nonce field
    wp_nonce_field('MyNonceAction', 'ticket_nonce');
    echo '
    <p>Ticket id:  <br />
    User id: <br /> 
    Description: <textarea class="widget" rows="4" cols="1" 
    name="ticket_description"></textarea>
    Priority: <select name="ticket_priority" placeholder="Select">
    <option value="critical">Critical</option>
    <option value="urgent">Urgent</option>
    <option value="important">Important</option>
    <option value="standard" selected>Standard</option>
    </select>
    Status: <select name="ticket_status" placeholder="Select">
    <option value="planned">Planned</option>
    <option value="in progress">In Progress</option>
    <option value="on hold">On Hold</option>
    <option value="completed">Completed</option>
    <option value="ready for invoice">Ready for Invoice</option>
    <option value="to be invoiced as per attached">To be invoiced as per  
    attached</option>
    </select>
    </p>
    <input type="submit" name="submit" value="submit">
    </form> 
    ';
}

And the below code is included in your theme / plugin core files, NOT in a stand-alone file:

if(isset($_POST['ticket_priority']))
{
    // Debugging output, since you are having troubles finding the issue.
    // If this doesn't fire, then you've got a problem with the select name or this code isn't included in your theme / plugin.
    echo "SAVING ENTRY";
    // Get the nonce value for validation
    $nonce = $_POST['ticket_nonce'];
    // If the nonce does not verify, do NOT process the form.
    if ( ! wp_verify_nonce($nonce, 'MyNonceAction')) {
         // If this spits out an error, that means the nonce failed
         echo 'Security error. Do not process the form.';
         return;
    }

    insert_row();
}

function insert_row()
{

    // You should use the WP table prefixes, so let's set that up....
    global $wpdb, $table_prefix;
    $tablename =  $table_prefix . 'st_support_ticket';

    $data = array( 
    'ticket_id' => '1', 
    'ticket_user_id' => '1', 
    'ticket_description' => $_POST['ticket_description'] ,
    'ticket_priority' => $_POST['ticket_priority'],
    'ticket_status' => $_POST['ticket_status'] );

    // Debugging: Lets see what we're trying to save
    var_dump($data);

    // FOR database SQL injection security, set up the formats
    $formats = array( 
        '%d', // ticket_id should be an integer
        '%d', // ticket_user_id should be an integer
        '%s', // ticket_description should be a string
        '%s', // ticket_priority should be an string
        '%s'  // ticket_status should be an string 
    ); 

    // Debugging: Turn on error reporting for db to see if there's a database error
    $wpdb->show_errors();
    // Actually attempt to insert the data
    $wpdb->insert($tablename, $data, $formats);
}