I have 3 computers on a LAN using an ADSL gateway. How to I connect my DSL route

Here's my situation. Sorry if I ramble - but I'm thoroughly stumped and want to give as much info as possible!

Our church has a 3 computer network. They all connect and play nicely over the network and are connected to each other via an ADSL Gateway. This is sitting on a rack down in our basement. Each can see the other and the file server (one of the the 3) in the basement.

We also have DSL, and that comes into the basement and connects to a router on a rack in the basement. I connect the DSL modem to the router and get a good green signal. Not flashing, but solid green.

When I run cable from the ethernet port on the DSL modem (signal out) to the rack router I am unable to get the computers on the network to recognize the internet connection provided by that modem. Any ideas?

Once I get THAT working, then I have to figure out how to get wireless connectivity through that connection so visitors can use our network when they're visiting our library or school. I could use some help with that also.

Calling the DSL provider would bust our already strained budget, so I'm trying to figure this out with help from the net.

Any and all help would be appreciated!