How to fix my old theme so it loads jQuery properly

Taking a stab at a general answer, since we don’t (yet?) have access to the specific Theme.

Note: all of these edits can – and perhaps should – be implemented via Child Theme.

First, you need to remove ALL of those lines from header.php. Scripts should be enqueued, rather than hard-coded into the template.

Then, you need to add the following to functions.php:

<?php
function wpse35169_enqueue_scripts() {
    // Enqueue WP-core bundled scripts
    wp_enqueue_script( 'jquery' );
    wp_enqueue_script( 'swfobject' );
    // Enqueue custom scripts
    wp_enqueue_script( 'jquery-inputs', get_template_directory_uri() . '/js/jquery.inputs.js', array( 'jquery' ) );
    wp_enqueue_script( 'jquery-scrollpane', get_template_directory_uri() . '/js/jquery.scrollpane.js', array( 'jquery' ) );
    wp_enqueue_script( 'jquery-mousewheel', get_template_directory_uri() . '/js/jquery.mousewheel.js', array( 'jquery' ) );
    wp_enqueue_script( 'jquery-easing', get_template_directory_uri() . '/js/jquery.easing.1.3.js', array( 'jquery' ) );
    wp_enqueue_script( 'jquery-lightbox', get_template_directory_uri() . '/js/jquery.lightbox-0.5.js' );
    wp_enqueue_script( 'wpse35169-functions', get_template_directory_uri() . '/js/functions.js' );
}
// Hook into 'wp_enqueue_scripts'
add_action( 'wp_enqueue_scripts', 'wpse35169_enqueue_scripts' );
?>

If you need a specific dependency/load order for lightbox or functions.js, just add the appropriate $deps array to the wp_enqueue_script() call.

That should resolve your issue – but again, without knowing what Theme you’re using, I can’t be 100% certain.

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