Hello bnelson101,
As per your description, it does not sound to be a problem with your Cisco Router. Your description is pointing to a problem with the Server.
Your computers should be able to ping the DNS Server.
DNS ports (TCP & UDP 53) should be allowed between computers and DNS Server.
Also, your local DNS Server should be able to send DNS Queries to public DNS Internet Servers and receive a response.
The Cisco 2901 is only providing the IP addressing automatically via DHCP and it sounds it is doing it properly.
Best Regards.