You can either do this on a PHP level or on a Javascript level. If you use Javascript, and/or JQuery, you can check and validate if all the checkboxes are checked with a selector...
Jquery also offers several validation libraries. Check out: http://jqueryvalidation.org/
The problem with using Javascript to validate is that it may be bypassed so it is wise to check on the server too.
Example using PHP and assuming you are calling a PO
<?php
if( $_GET["BoxSelect"] )
{
//Process your form here
// Save to database, send email, redirect...
} else {
// Return an error and do not anything
echo "Checkbox is missing";
exit();
}
?>