Unable to add JavaScript on a page
This should do it:

function MYTHEME_preprocess_page(&amp;$vars) {
  if (drupal_is_front_page()) {
    drupal_add_js(drupal_get_path('theme', 'MYTHEME') . '/MYSCRIPTS/myscript.js');
    $vars['scripts'] = drupal_get_js();
  }
}


FYI:  You'd use drupal_get_js in case any modules are also using hook_preprocess_page and setting new scripts themselves.

Also, I wouldn't just add a newer version of jQuery in willy nilly.  Try either jQuery Update or jQuery Multi