What I am trying to accomplish is to allow the devices (mainly the computer) connected to the second router to see the computer (and any other device I connect later) to the first gateway. Currently the second router has its own network and cannot see what is outside it. The second router is obtaining the internet connection from the gateway. The second router has gaming devices connected as well, but that is less important if they can see the devices connected to the first gateway.
*UPDATE*
I was able to get the computers to see each other. My problem now is when the second computer tries to access the first, it says:
"[The computer name] is not accessible. You might not have permission to use this network resource. Contact the administrator of this server to find out if you have access permissions. The network path was not found."
I think it may have to do with file sharing issues, so I will check into that.
For those of you interested, the way I was able to get the computers to see each other was, on the second router:
Turn of DHCP
Change to Router mode
Change IP address to be different from first router
Change Ethernet cable from gateway to plug into LAN port instead of WAN port
Restart computer and router
Changing the cable to be plugged into a LAN port was what took me forever to figure out. Thanks for everyone's help. Hopefully I just need to check the file sharing options on the first computer to get this to work!
*UPDATE*
Well I have the file sharing fixed and everything seems to be working fine.