At a guess, it's your routing table that's causing problems. If you have the two devices, you'll need to tell your system you wish to use eth0 for Internet connections, and wlan0 for your internal network connections.
For example, if my default gateway (Internet connection) is 192.168.1.1, I would type:
route add default gw 192.168.1.1 dev eth0
It's the last bit which is crucial, as this tells the system it needs to use the device eth0 for Internet communications.
Hopefully this will let you use both devices at once