Well, this is somewhat of a mystery since with most problems it will do one of those three, which enables us to diagnose it.

In your case, it is not agitating, spinning or draining, but the clicking sound makes it seem like the motor is turning, and your pump is just a mechanical device driven by the motor so it should at least drain. Since it is not the most likely problem is an obstruction in the pump which is jamming everything up. Take off the cabinet and the pump and check it out.

If this is not the problem, go ahead and take off the motor and see if the transmission will turn. It could be your transmission is jammed in some what preventing everything from working, but let's hope its the pump, cheaper and easier to fix.

Here is a video which will show you how to open it up.

YouTube - Direct Drive Washing Machine Repair Video Tutorial *Watch in HIGH Quality!*