CLI stands for command line interface. For example, you can run the Gnome Terminal program and then enter:
This command will list all of your network interfaces. The wireless interface may have the name "wlan0".
If there is an IP address listed on the second line for wlan0, then you have an IP address.
GUI stands for Graphical User interface. Firefox is a GUI program. Where as `ping' is a cli program.
It would be a good idea to check whether your wireless device is working, and can see Access Points (APs). If your connection tool was able to scan for APs and list them, that indicates that your device and device drivers work. The following program will scan for APs. It is provided by the wireless-tools package. You probably already have it installed, but if the command can't be found, then use your package manager to install it.
sudo /usr/sbin/iwlist <wireless device> scan
Your wireless device is most likely named "wlan0". If so then the command is:
sudo /usr/sbin/iwlist wlan0 scan
Report the results. If you don't see any APs, then we need to move backwards and see why the wireless device isn't working. If you do see APs working, we can look forward and look at the WEP configuration.
Also indicate if you use DHCP.