<p>I have a server with .Net 2.0 sp1 installed and have no ability to  install the AJAX extensions on the server.  </p>

<p>Is there anyway I could work around this to incorporate ASP.NET AJAX functionality?</p>

If you can't install AJAX extensions, you will have to manage the AJAX calls yourself.  It's absolutely possible, since AJAX Extensions just wrap the meat of AJAX.  Read up on XMLHttpRequest and you'll find many examples.
Here's a good site with examples.
http://www.fiftyfoureleven.com/resources/programming/xmlhttprequest/examples