Browser problem with CiviCRM upgrade

I'm trying to upgrade CiviCRM from 3.2.4 to 3.3.2 on my test site. The CiviCRM black navigation bar across the top is broken in some browsers but not others -- the text entry box with the magnifying glass is missing, nothing happens when I click on any of the top menu items, and none of the child menu items display.

I THINK the problem is with software the browsers use because the problem occurs with Firefox 3.6.13 on my laptop, but it does NOT occur with Firefox 3.6.13 on my notepad. The menu bar works on my laptop with Google Chrome 8.0.552.224 and Safari 5.0.1 but not with Firefox 3.6.13 or Internet Explorer 8 or 7. With Internet Explorer (8 on laptop and 7 on notepad), the theme is broken -- the CiviCRM pages display as one column of text and links. The Drupal pages are normal. I'm using the theme Garland.

BUT... Firefox and IE work fine with the CiviCRM demo site -- demo.civicrm.org. Most perplexing! Could there be something strange with Javascript somewhere?

You can see what's happening -- go to http://test.nccommunities.org, login as demo with password demo and click CiviCRM.

I tried a couple of weeks ago to upgrade from 3.2.4 to 3.3.1 and ran into the menu problem though the theme worked OK in IE. I found http://forum.civicrm.org/index.php/topic,17442.0.html which includes "This is already fixed and will be part of 3.3.2 release. ( http://issues.civicrm.org/jira/browse/CRM-7202 )" so I went back to 3.2.4 and waited for 3.3.2.

I suspect this is a browser problem, not a problem with CiviCRM. My skills are quite limited. I don't know anything about browsers or Javascript.