I didn't get the .htaccess file, but If the .htaccess is ok, then it's either a plugin redirecting the request, or the Apache vconf files are causing it.
The url http://quiquealien.com/wp-admin/admin-ajax.php should return a “0” if you open it in the browser, but it does not, it's redirected to a 404 error page.
You can try deactivating a few plugins (mainly cache plugins) to see if any of them is causing this. The 404 problem is unfortunately not related to Ajax Search Pro, so I honestly don't know what might exactly cause it.Best,
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