First make sure that the Wireless work OK without security.
Set the security to the desired/possible level in the Wireless Router and generate a Key, then you set the laptop with the same key.
Do not turn off your SSID, it might destabilize the connection, and it is No adding any security.
http://www.ezlan.net/faq.html#ssid
When you are in a public places if the Hot Spot is open you have to temporary disable the security on your laptop.
Otherwise, ask Da Man in charge what the security configuration is? If your Wireless Utility shows Secure Wireless, you need to get the password from the owner of the Hot Spot.
If you opt (or forced) to use WEP encryption read this,
http://www.ezlan.net/faq.html#wep
If you see in the configuration menus a reference to 802.11x authentication leave it unchecked, it is used in the business world with special logon servers.
From the weakest to the strongest, Wireless security capacity is.
No Security
MAC______(Band Aid if nothing else is available).
WEP64____(Easy, to "Brake" by knowledgeable people).
WEP128___(A little Harder, but "Hackable" too).
WPA-PSK__(Very Hard to Brake ).
WPA-AES__(Not functionally Breakable)
WPA2____ (Not functionally Breakable).
Note 1: WPA-AES the the current entry level rendition of WPA2.
Note 2: If you use WinXP and did not updated it you would have to download the WPA2 patch from Microsoft.
http://support.microsoft.com/kb/893357
The documentation of your Wireless devices (Wireless Router, and Wireless Computer's Card) should state the type of security that is available with your Wireless hardware.
All devices MUST be set to the same security level using the same pass phrase.
Therefore the security must be set according what ever is the best possible of one of the Wireless devices.
I.e. even if most of your system might be capable to be configured to the max. with WPA2, but one device is only capable to be configured to max . of WEP, to whole system must be configured to WEP.
If you need more good security and one device (like a Wireless card that can do WEP only) is holding better security for the whole Network, replace the device with a better one.
Setting Wireless Security -
http://www.ezlan.net/Wireless_Security.html
The Core differences between WEP, WPA, and WPA2 -
http://www.ezlan.net/wpa_wep.html