well, that's not hard. You should create a new .php (dynamic) block (please note, changing your existing block's filename from html to php will not work, so create a new one) with the following code:
//Check if the user is logged in and show your html code taken from template
if ( isset($_SESSION['user']) && !empty($_SESSION['user']) )
{
$tpl->define( 'tpl'.$id, 'block_digby.html' );
$tpl->parse( $id, 'tpl'.$id );
}
else
$tpl->assign( $id, '' );
Now you should move html code from your original block to the "block_digby.html" template which must be saved in the templates' folder.