Sounds like something is jamming it (spilled soda). Here's a good vid on how to take off the speed dial: [https://www.youtube.com/watch?annotation_id=annotation_2975304121&feature=iv&index=5&list=PLbBpUKJh6LCmx4zwCUEg5dCoIraoFd8LS&src_vid=Vonx87C1zvU&v=sHgN1RM3H7c#t=27s|Fix Old Cameras: AE-1 Top Cover Removal / Battery Door Replacement]
Now with the speed dial off you can take the knob apart to bathe it with a good household cleaner.
Do be careful as the ASA linkage (cable and pulleys) to the other side can easily be damaged when you release the tension of the dial.