Lets do a couple tests:
Pull up a command prompt and enter "ipconfig" ... near the middle of the page you will see "default gateway". Make note of that IP address.
Using the command prompt, enter "ping x.x.x.x" where the x.x is the address of the default gateway. If this works, then you are connecting to the router.
Using the command prompt, enter "ping 8.8.8.8" (this is a google server). If this works, then you are connected to the internet.
Using the command prompt, enter "ping google.com". If this works, then we have something odd going on.
My guess is the last test will fail and it's because your not getting DNS server information from your DHCP. You may have to enter it manually.
The other possibility is a network issue caused by the 2 routers. You didn't really say how the routers were setup, but I assume you are running a line from one of the lan ports of the main router to the wan port of the 2nd router. The causes you to do NAT twice and weird things can happen, especially if both are on the same network (192.168.1.x, for example). It might be worth considering changing the 2nd router to bridge mode or moving the incoming ethernet line from the wan port to a lan port. This will turn your 2nd router into a switch than can do WiFi and your main router will do all the NAT, DHCP, firewall, etc ... unless you have a reason to have 2 networks.
Let us know.