How can I fix my White Westinghouse Model LA560M Washer?

My Washer does not engage in the spin-cycle. I suspected this a few times before as laundry was pretty wet on occassion after the rinse cycle was complete. It is pretty old, but having just become unemployed and it is the Holidays I want to see if I can do anything simple to stretch its usefullness.
I already changed the belt. When the washer is to be in the spin-cycle (but it is not spinning) I use the handle from my mallet to push tension on the belt until I hear a click, then I let go. The tub then begins to spin.
What is causing this and what can I do to repair?