WEP is no really security.
Try this.
In Windows click on the Wireless networking Icon in the notification area and select Open Network and sharing center. Then click on Manage Wireless Networks. In the windows that open do you see the SSID for your router? If you do Right Click on it and select Properties. In the dialog windows that open on the Connection tab "Connect automatically when this network is in range" should be checked. Then go to the Security Tab and make sure the security type is set to what your router is set to, click the option to Show Characters and make sure the password is set correctly.
If it still fails to get a valid IP address from the routers DHCP server then I suggest you change the routers wireless settings. Change the SSID and set the security to WPA2-Personal and change the password. Then go back to the computer and try to logon to that new SSID using the new password you set.