How do I setup for WAN and LAN with 2 router2?

1)I have a computer which is connected to router1 (wireless USB) for internet activities.
2)The same computer is also connect to another router2 (wired) for LAN gaming, filesharing, etc...

The problem I'm having is that I kept on losing access to Router1 everytime I turn router2 on or plug router2 to the computer. The sytem tray icons (shown in the bottom-right of the window's screens) shows connected for both routers when both are on, but only have access to router2. When I disconnect router2, then my router1 would allow me to access the internet else no internet access. Basically, it's one or the other router per time.

What should I do in order to be able to have get access to both as the same time?

Any Ideas would be greatly helpful.