Reading this made me soooooo thankful that my MBA is finally complete (just finished 2 months ago)

I've been there in trying to find internet access including this last trip which involved taking 2 laptops (1 for work and 1 for classes).
Anyways, there are NO public access computers at the WL. If you choose not to take a laptop you would have to go do one of the "convention" hotels and use their business center. The two that I am aware of are Contemporary and Coronado Springs. As the Contemporary is only a quick boat ride away it would be your best bet. However, the times are sometimes not the greatest.
Also it can be quite costly. If you post this as a question on the esort board someone should be able to answer the cost or provide you with a phone # for the resort to ask the business center.
IMO if you need internet access I'd lug the laptop. Good luck!