Without going into too much detail about networking, the basic problem is, assuming you are using the default settings, each router is set to use 192.168.1.1 as thir IP, and each router is attempting to act as the DHCP server. This conflict is why the devices connected to the second router are not functioning. Simple fix however.
- Connect your computer directly to the second router(the one without the modem), and log into the router's configuraiton page, normally http://192.168.1.1, if that does not work check your manual. On the status page, you will need to change the IP address of the router to 192.168.1.2 (Instead of the old 192.168.1.1).
- You will also need to disable the DHCP server on the second router. This should be on the same page of the IP, but once again if not consult the manual.
- Now connect the two routers together using a standard ethernet crossover cable, but make sure to plug each end of the wire into one of the four device plugs, and NOT into the WAN/Internet uplink port.
That should do it, you have now configured your second router to act as a switch, rather than a router. This will now simply forward the traffic from any devices onto the router. For example the internet traffic will go from the device, through the switch, to the router and out to your ISP. Look forward to hearing back with a notice of success. - Sub
*Edit - One last thing. When you are done, you will need visit the configuration page for your first router. Under the DCHP server options, change the "Starting IP Address" to 192.168.1.3. This will make sure the router does not accidently assign a device the IP address of your second router.