I've had very good luck using a high-nap towel or microfiber cloth and a little cleaning solution to fix this issue:
1. Dampen one section of the towel or cloth with some iKlear, windex, or water. You want a slightly damp area and a dry area.
2. place the towel on a hard level surface, turn the mouse upside down and roll the scroll ball vigorously in all directions for several minutes, alternating between the damp and dry areas.
3. Test for restored function, repeat as necessary.
BTW: I've taken a few completely failed mighty mice apart, but the newer ones have plastic weld tabs on the bottom ring, making it almost impossible to reassemble the device in a working manner - the ring is the gliding contact point for the bottom of the mouse, so it has to be level and firmly attached.