Javascript assumed conflict with Drupal
You should use the jQuery provided by Drupal and try to work with what Drupal provides (JavaScript, Form API, Theme system, etc.) instead of trying to work without it or, worse, against it. The jQuery update module allow you to use updated jQuery releases in Drupal. That would be 1.6.2 for Drupal 7 and 1.3.2 for Drupal 6. Drupal 7 also provides jQuery UI while for Drupal 6, the jQuery UI module should be used to provide it. This way you can avoid compatibility issues between different version of the same library, unnecessary workarounds and fixes over fixes.

Also, you shouldn't use $(document).ready() in Drupal, but add your function to Drupal.behaviors as explained in the Drupal JavaScript API guide (also available for Drupal 6). And off course, for the form generation, validation and submission server-side code, you should use the Form API. 

Keep in mind that your are trying to add a form to a Drupal site, not to a stand alone simple PHP script that doesn't already provides all the (server-side) API your need.