I have a problem with my wireless Internet connection?

Most likely a misconfiguration between your wifi router and your laptop's card. Since you've established that you can connect to an unsecure signal that means your router and laptop can communicate and all the equipment is working. I would try step wise setting up the simples form of wep. Wep 64 bits, with a simple key like all 0's , keep everything basic, and try to apply the changes to both sides. Its possible but unlikley your one of the few folks that has a strange and incompatible wifi router and laptop, if possible consider replacing your router, you can find them as low as $35 at local stores..