The WEP/WAP security code is setup within your wireless router. Who ever setup has the code. If no one remebers it just reset it by logging into your wireless router and change it. Follow the instructions for your make and model.
When using the LAN adaptor make sure to make a new internet connection and choose Wired connection. If that still doesn't work then you'll need to check your router settings. There are many security options and it might be setup to allow only so many devices or MAC address. If all else fails and you have no idea who setup then, then just reset the unit back to default settings which will disable all security settings.