The short answer to your question is yes you can, but NOT as you are currently configured.
Issues:
DNS: Your server hopefully has a static IP address. Otherwise AD will not operate properly. You also need to have a local DNS server in orderfor AD to work properly. AD requires a DNS server that is capable of dynamic updates. This is because AD creates many extra entries in DNS as part of AD configuration. MOST ISP DNS servers either don't have, or won't allow this capability. You mayhave AD installed, but it is not working properly (try setting up another DC - I guarentee it won't work). Install and configure DNS locally! Your DNS server needs to point to itself for DNS. You need to add your ISP's DNS server in the Forwarders section of DNS configuration. All clients need to point to your local DNS server (either hard-coded or through DHCP - see below).
DHCP: If your clients are receiving DHCP leases from your router instead of an internal DHCP server, they are receiving DNS information relating to your ISP instead of DNS information that relates to your domain. You need to install, configure, and authorize DHCP on your DC and turn off the DHCP capability on the router.
WINS: If any of your clients are running any operating system prior to Win2K, you really need to have WINS installed and running in order for your clients to be be able to browse the network consistantly.
Let me know if you need clarification on anything.