There could be several issues going on here. First of all, the easiest thing to do would be to go to the wp admin and visit the permalinks page. You may or may not need to press the save button twice.
Also, check your .htaccess file for any redirecting to the old domain.
I think what your issue is, though, is probably an old value for home and site URLs. You may be able to change this in the settings > general tab, but if not, you have to go into phpMyAdmin. Look for the wp_options table, and find the row for home_url and site_url. Make sure those two values are not pointing to your old site.
Lastly make sure everything is pointed properly in your web tools…the A records and such.