|During the promotion process you will be asked to configure DNS. When you're finished, you will need to setup DNS forwarding on the DC. Just forward your internal DNS to your providers DNS server(s). This will allow for resolution of requests outside the local zone.|
Internal (domain) clients should point at the DC for their DNS. Local requests, such as logging in to the domain, will be processed by the DC's DNS. Requests outside the local zone will be forwarded to your provider's DNS.
Currently its a simple DSL connection, one router/DSL modem combo and 3 switches that divide the connection.
In a situation like this, I disable DHCP on the router and use the DHCP service on the DC instead. Configure your scope and when you do so, ensure the DNS address you give out is the DC's IP. If you have DHCP enabled on both the router and DC you're going to have problems. Best practice is to have just one DHCP server.
You need to concentrate on the DC first. Once you've gone through the promotion process and forwarded DNS, ensure your DC is getting internet connectivity before trying to create any domain clients. Once you have the DC up and running and connecting properly to the internet, then join a client to the domain and ensure it's getting proper internet access.