Mary,
You absolutely can take a laptop computer into the Disney Theme Parks!
I will admit that I have taken a work meeting or two from within the parks, when it was necessary. The real key is finding a quiet place to get work done, especially if you are going on a video conference call. I have found several good places in the
EPCOT World Showcase. The United Kingdom pavilion has quiet areas by the waterfront, as well as back in the courtyard.
BONUS TIP: Lockers! But what if you do not want to carry your laptop around all day? No worries! In each park there are
lockers available to rent. They are at the front of each park after passing through the turnstiles, and there are a few locker sizes available. They are keyless and typically will cost you $15 or less for the day. The
Magic Kingdom Park and EPCOT even have a few larger lockers available that are up to 17" x 22" x 26" (43 cm x 55 cm x 66 cm). Prices can change, so check first online for current rates.
Write me back if you have any follow-up questions.
Have a Magical Vacation!Doug