Pull the unit away from the wall and lean it back. You will see the belt and the pulleys on the bottom. If it is not spinning, it will probably need a thrust bearing kit installed. Look for a melted plastic piece on the middle pulley. I have included a picture of the assembly to help you out. The thrust bearing kit is number 24 in the pic and the part number is XXXXX It is not a super hard replacement but, if the belt doesn't help and the middle part is melted, it is your only choice. Let me know if you have any other questions.
So it will not drain. That is different. Is the tub spinning at all?
If the pump is draining when it does spin then it definitely sounds like the thrust bearing kit on your unit. This kit will seize up and will not release the brake package sometimes. It is a design flaw on most of the Maytag units that were built this way. This will have to be replaced in order to get you unit functioning correctly.
No. If you are fairly handy and can follow the instructions in the bag, you can do it. No reason to pay a tech 100+ dollars to do it for you.