Sounds like you need a new timer.  Motor is working but the escapement isn't catching.  It happens to a 35 year-old machine! :)

The Maytag part number for that timer is 2-4476 which is often changed to 204476.  These timers aren't cheap (expect to pay in the $75-100 range).  Search on the interwebs and see what you can find.  I bet you can get a decent deal if you shop around.  I can email you the service manual for this machine if you want it.  Mark. 

As Mark says, you seem to have an issue with your timer, but it may be something you can fix. These timers aren't complicated and if you'll have a look at the photo below I'll point a few things out to you.

First off, the red arrow is pointing to the actual motor. All it does is advance the timer, and if it's failed it can be replaced.

The yellow arrow is pointing to the top end of a plastic pin that's mounted off center on a rotating disc. This disc is turned by(and part of) the timer motor. As the disc rotates the pin moves around in a circle, and as it does it advances and retracts the plastic arm indicated by the blue arrow. When that plastic arm advances it pushes against a little cog on a Bakelite disc which rotates the timer forward  one small increment. If that plastic pin has broken off, even though you can still hear the timer motor the timer will no longer function, and even though the timer motor still runs, I'd consider this a timer motor failure.

The green arrows are pointing to a wire spring that's hooked under a tab at the tail end of the plastic arm. That tab is located at the spot indicated by the dark green arrow, and if the tab has broken off or the spring has somehow come loose, the timer motor will run but the timer will no longer function properly.

So here's my opinion. The fact that you can make the machine function by manually advancing the timer tells me there's probably nothing wrong with any of the timers cams or switches. If any of the Bakelite cogs had broken off of the cam disc, that could cause the timer to stall when it got to that point, but once you manually advanced it past that point it would resume its normal function, so that's unlikely. So my guess is something's gone wrong with the plastic drive pin on the motor, or there's an issue with the wire spring, or there's an issue with the plastic arm that advances the timer.

Any of these issues are easily corrected without spending a great deal of money, and as it happens I have several severely dead timers of this type that have these parts if you end up needing them. If you decide to take the timer off to get a better look at it, it's held in place by two screws hidden from view under the timer dial. They fit in the holes indicated by the white arrows.

I hope this helps.