What browser are you using?
Some browsers will not Ajax from a file on your computer. You
need a server.
Also, there can be issues with same-origin policy. The directory
on your computer from which the page was loaded is considered the
"origin". You cannot load a page from outside of the origin
(up to a higher directory, on a different drive, etc.) either with or
without Ajax. Your browser may have a setting to defeat this - usually
a hidden setting.
Every browser is different about this. Some are more permissive
than others. You can force Chrome to change the policy with a hidden
setting. Safari just works (when origin is a file on your filesystem).
I guess Apple figures if you are loading it from your filesystem, you
know what you are doing, no reason to enforce a policy. If the origin
is a website, though, it is enforced, and you can see why... it could
be easily abused by websites. A website could get access to your
private files!
Why not just install a server, and test under realistic
conditions? They are easy to install, you can get a simple install
package for any OS.