What you really need to do is disable any security or encryption, like WEP, on both the access point and the computer and just get it to connect using basic settings.
If you can connect without using security, then chances are you are incorrectly entering the encryption key, or some other settings.
If you cannot connect without security, then are both the access point and the network adapter made by D-Link? If not, you may be facing a compatibility issue between the two. A firmware update to one or both could clear that up, check with the manufacturers of the products.
If they are both D-Link, then there could be a hardware problem. In which case I would ask, can other wireless computers connect to this access point, and can this wireless computer connect to other access points?