You've probably already done it, but you might check for driver updates for your network adapter. From your description, I'm not sure it'* a hardware problem.
Since you are doing a full backup, this might be a good time to reformat and reinstall your OS - since the first version of windows, all the way through XP (and I'm guessing Vista), it'* been my experience that a periodic format and reinstall is required. Well, required is the wrong word, but it'* the quickest way to get back to a normal state, AFAIAC.
If all else fails, you should be able to get a PCMCIA network card. I don't deal with laptops much, so I don't even know if PCMCIA is still the standard - but there should be an accessory slot for things like this.
94 Bonneville SSE