A DNS error message like that doesn't say much. It could be a problem in the DNS servers of your hosting company, or it could be that moving your site menat that you had a different IP and sometimes, not always, it means a DNS change which need to be reflected in your domain company (specially if you bought your domain name with one provider and you host with other).
The only thing that you can do is checking the DNS servers that should be configured for your domain (normally, you can find this information in your hosting provider's faqs or support pages).
Then log in in your domaing provider website and check that those servers are the one listed for your domain.
If they are, then it is possibly a temporary problem. When DNS servers are changed, it takes a few hours to propagate that information through the internet but in certain cases it could be up to 48 hours.