First, I must apologise for the huge delay with this response. I've been busy with other things (visiting my other half in Sweden) and checking back here at Cable Forum in regards to this problem completely slipped my mind. I really appreciate both of your advice though and thank you for that- but I'm happy to say the problem is now fixed.
I decided to forget the D-Link drivers and instead installed ones from Ralink. Apparently, the D-Link USB Adapter hardware uses Ralink's chipset, therefore installing the Ralink drivers should in theory still get it working- and it did!
Despite now connecting to my home network, the device itself kept mysteriously ejecting from my computer (with the OS beeping whenever it did, and then beeping again once it'd reconnected itself.) I fixed this by simply taking the device out of the USB adapter it came with (they're rubbish) and plugged it in directly. I wouldn't advise using it at all, just plug the D-Link device straight into USB, forget the crummy adapter!
Apologies again for the late reply.