There are two possible reasons:

1. Your template or another script is preventing MooTools from loading;
2. There is a javascript incompatibility;

Ajax Contact uses MooTools to validate the form and to perform the AJAX calls;

MooTools is the Joomla default javascript library, therefore most templates use MooTools for their fancy things such as menus and slideshows; Your template or other extensions (modules, plugins, components) shouldn't use another javascript library other than MooTools, however if it does use another library such as JQuery it might be incompatible with many MooTools based scripts;

Solution:

Disable the extension that is loading this other javascript library.

Advice:

Always choose extensions that are 100% compatible with Joomla Framework;