I agree with the poncho idea-you planned too hard and too long to sit in the room. However...here are some things to try besides running in the parks in the rain:
Visit the different hotels. My family and I make a habit of getting on the monerail and riding it to the Contemporary-there we like to stroll around the hotel and look at the different shops inside and do some shopping, even though we've been there several times, there's always something new to look at and buy in the stores. From there, we do the same thing with the Polynesian and Grand Floridian Hotels-shopping, walking around them, etc. Also, if you don't mind the buses, hop on a bus heading to a different hotel other than the one you're staying at from the park, and explore that hotel.
Try Downtown Disney. A bus can get you there, and there's a heck-a lot to do. There's always shopping, and lots to eat, so you can enjoy a meal, and then you can head over to Disney Quest-that's where you can take an art class and learn to draw Donald Duck, and design and ride your own rollercoaster.
If you are still gung-ho about going to the parks, but want to try and stay out of the rain-there's always shopping in the Magic Kingdom down Main Street USA. A little known, or little realized fact, to most first-timers is that most of the stores on Main Street connect to one another, so you can get down the street a fair distance without ever having to set foot outside in the rain.
If you should decide to forge the rapids and set out in a poncho or opt to stay indoors and get the souvenir shopping done, either way, make the most of your trip and enjoy it! Just stay away from the large Minnie/Mickey shaped balloons. If you buy one and it gets rained on-the paint on it WILL CHIP OFF and get all over you. That's from a personal Disney in the Rain experience.
