Hi,
ping first looks for the hostname in /etc/hosts and if it finds it there is does not use a dns to resolve the hostname to the ip address. I guess that's the reason ping works regardless if you can visit your site.
The fact that one isp can't resolve your host while the other can, could be that the domain data is not yet propagated.
To check your dns settings, put your domain name
here and see if it reports any error
Regards