It's a good idea to remove the cabinet, drop the pump and motor from the tranny and see if the tranny drive lug is hard to turn manually. This goes for the pump in front of the motor as well. They can bind up and cause the motor to drag down just the same. You can also bypass the lid switch while the cabinet is off and run the motor by itself while it is lying on the floor away from the tranny to see if it behaves the same way with no load on it.
Despite its age and usage, a new motor or tranny is a heck of a lot cheaper than a new washer, so why would you not want to pour some money into it? Age has nada to do with it and buying a new washer does not give you any less chance of a breakdown these days..