There are several tutorials online that will show you how to clean the trackball on your older BlackBerry device. The short version is this: you may be able to remove the trackball without taking the device apart. You can probably pry the plastic rim that surrounds the trackball and pop the ball out. That's what I did the other day. I simply used my fingernails to pry around the silver ring and then I carefully removed the ball. After some cleaning, the trackball worked just fine!
If you're having some problems using the trackball on your older BlackBerry, just clean it carefully. (Oh, and if your desktop computer uses a mouse that has a ball, you can clean that too.)