If you set the DNS server option in your DHCP to the DNS server of your ISP you might run into problems with USER authing to the DC. I would recommend that you DELETE the . domain from the DNS records and then use the forwarders option in the DNS properties. You simply set the DNS servers of your ISP as the forwarders and still have the DNS option of YOUR DHCP set to the Domain Controller. When your DNS server doesnt know google.com it will look at those forwarders for the answer.
you can find the dns servers from your isp without calling them by logging into the switch/nat and looking at the options that it has recieved from the DHCP of the isp.
