I believe that what you want to do is use DHCP which can assign an IP address, gateway, and DNS server addresses to computers on your network automatically. Many DSL routers include this functionality.
Normally a T1 router does not handle DHCP and the 2824 like most switches does not either. It can act as a DHCP relay but that's a feature typically used for remote locations of larger networks.
There are a couple of different ways to handle this.
1. You may be able to use your old DSL router for this role but only if it will allow you to set the gateway address to an address that doesn't match its own, i.e. the gateway address given to all clients by DHCP must be the internal address of the ADTRAN router.
2. If you have a server like MS Small Business Server then it can handle the DHCP.
3. If neither of the above are practical, you can install 3rd party DHCP server software on a PC. Here's a link to some info on doing this for windows:
http://www.tomshardware.com/forum/13577-43-dhcp-server-windows Be aware that if the machine serving DHCP goes down, so will your network after a period of time.
4. I don't recommend using APIPA which is the last ditch method of automatically assigning a 169.254.0.0 network address to PCs when a DHCP server can't be found. You could make this work by giving the router an internal address on the 169.254.0,0 network but you would need to manually configure the gateway and DNS server addresses to make this work.
Regardless of how you handle this, be careful to use a private address range for your side of the router. For a network your size you would normally assign a 192.168.0.0 address with a subnet mask of 255.255.255.0