If you hide your SSID no computer, your own included will normally be able to see the network. However, that isn't a problem as long as your network name is easy for you to remember.
Rather than trying to connect through the 'show visible wireless networks' screen, you need to tick on the 'set up a wireless network for a home or small office' button. Once you do that, a wizard starts up and you can enter your SSID and security key (as long as you can remember them both) and you will connect quite cheerfully.
It's a little more complex than doing it straight from the networks screen, but not much and it gives you more security.
If you are not sure why you should hide your SSID this quote from this month's PC Pro might help:
By default all access points come pre-configured with a standard name known as an SSID wich the access point merrily broadcasts to all and sundry, allowing clients to see that there's an access point to connet to This is very usful in Starbucks, but the last thing you want in your home setup. So you should do two things; first change the default SSID; and second, hide it by instructing the router not to broadcast its presence.
This makes it much more dificult for anyone to find and start attacking your setup. It's as easy as pie and simply requires that you think of a name and check the 'hide SSID' option which your router will have in its web-based configuration.