On wireless networks, there are 2 stages of connecting. The first is associating with the Access Point. The seconds is properly authenticating to the Access Point. It sounds like the first stage is happening fine. The seconds stage (encryption) is where it sounds you are having the problem.
With out successful authentication in the 2nd stage, you will not be connected to the rest of the network. The reason why you cannot get out to the Internet is probably because your laptop never received an IP address via DHCP. This can be confirmed by opening a command prompt (start -> run -> Type "cmd" (No Quotes) -> Hit OK) and executing the following command:
ipconfig /all
You should have a 192.168.x.x IP address. If you have an address in the 169.254.x.x or 0.0.0.0 range, then your laptop did not receive and IP address and will not get out to the Internet.
The cause for you not getting an IP address is most likey due to the encryption keys not EXACTLY matching. This often happens when using different vendors products, as their implementations are not always EXACTLY the same.
From what you mentioned above, 16 bit WEP key does not sound like a standard length. They are typically 10 or 26 bit. What I would recommend is that you set your wireless clients and wireless router to the EXACT same settings. When doing this, do not use pass-phrases or ascii characters, as different vendors may produce different keys, and this may be causing your problem. What you want to use is a 10 or 26 character string of the digits 0-9 and the letters a-f. This is known as a hexidecimal string. This is the one sure way you will have exact matches on both sides. One example of a 26-bit WEP key would be the following:
8005532447badfad8005532447
Note: The letters can be uppercase or lowercase. Hexidecimal characters are case insensitive.
