First you hoster needs to be aware that he should serve that domain. If he is not then the webserver won't know what to do with the request even if all DNS settings are correct.
If you have a domain hosted at hostgator, get its DNS vlaues over
http://www.zoneedit.com/lookup.html.
Enter as domain name you domain without www and search type any. There you should get the A record and MX record you need. Enter the same values in your new domain.