Ajax PHP form working perfectly on-site located by Bluehost
No longer working when used to goDaddy?
Are you currently while using free hosting plan that you will get whenever you register a website? They indiscriminately add their ads to any or all outgoing HTTP streams no matter content type, which effectively breaks any non-HTML.
Try setting up something like Firebug to see what's returning and forth within the wire. My prediction is the fact that you are getting malformed XML or JSON (or whatever other data encoding you are using around the AJAX service).
Missing any significant info inside your question, my best guess would be that the PHP script is failing, which could happen for a variety of reasons. One of the most likely problems is attempting to utilize a function or library unavailable within the version of PHP placed on the webserver. Also, you cannot (automatically) Ajax to some script on another server, when was your intention.