Hi, you shouldn't be clicking on Network. That is your network PC, probably your home PC. If it is not switched on, you won't be able to mount it. And if you haven't configured your wireless, you won't connect to anything.
You should see a wireless signal icon in your system tray. Right click it and it should show you which wireless networks are available. Just select your network and enter your WEP, or whatever. If you don't have a wireless icon running, do you have a manual switch for wireless? Try that.
I am a newbie, so don't know anymore than this sort of superficial stuff. However, if you want to know how to manually start the wifi service, search around for the command. I am sure it will be out there.
I am using an old Acer TravelMate 3200 and Mint is just great on this. I also use it as a live CD on my EEE Pc, running from a 4Gb SD card.
I think Mint is an absolutely fantastic find. It has allowed me to solve a problem I had with an O2 3G dongle that was not recognised in my EEE Pc Linux-based OS.
It has also given new life to what would be considered a tired old laptop.
Mint 7 full install off 16GB SD card in EEE PC 701 4GB. Mint 7 full install on Acer TravelMate 3200.