Just go to the Business Center. If you are staying at the hotel and it only takes a few minutes, I am sure that they will not charge you to use a computer. BTW ... the cast member computers are internal computers and are blocked by Disney to many websites to avoid virus' (ie: they cannot check their yahoo, hotmail, etc, on company computers). The Business Center computers are not networked.
The Business Center is located near the hotel enterance to DTD. If you have paid for Concierge services at the hotel, they also have a non-networked computer and printer in the Craftsmans Club for use by Concierge guests.