$.ajax call working fine in IE8 and Doesn't work in firefox and chrome browsers

this is because of the Same origin policy. you cannot use ajax to call external sites. if you really want to use, you have to use JSONP. Or you can use serverside proxy for this. means, call external site in the server side and do ajax call to the that webservice.

UPDATE:

create webserveice in your site and in the webmethod put following code

string proxyURL = "http://devserver:7995/stdpart/services/GetAllPartsWithFilter";
HttpWebRequest request = (HttpWebRequest)WebRequest.Create(proxyURL);
request.Method = "GET";
HttpWebResponse response = (HttpWebResponse)request.GetResponse();

if (response.StatusCode.ToString().ToLower() == "ok")
{
    Stream content = response.GetResponseStream();
    StreamReader contentReader = new StreamReader(content);         
    return contentReader.ReadToEnd();
}
return string.Empty;

then access local service using your code.

for more information please refer this link

Another solution would be to use the jQuery ajaxTransport extension that uses XDomainRequest for IE8+.