Pump?
The motor on your washer is probably in the front left corner. If so, the pump would be in the front right corner. These Maytags work by having the motor turn one way for agitation and then reverse for spinning and draining. This means that the pump also changes direction. Check and see if your pump is seized.
The motor is on a sliding spring-loaded mount. To check the pump and belts, tilt the machine back (laying it on its back is not necessary) and prop it SECURELY in place. This will release tension on the belts on the bottom of the machine. The double pulley is the motor, the big pulley in the center is the transmission, and the small single pulley in the corner is the pump. Pull off the belts, since they will be slack, and give the pump pulley a few turns by hand. Will it move? If it moves easily, your pump is probably fine, unless it is leaking. Replacing the pump is pretty easy, it is a commonly available part and it's not very expensive. Put the belts back on in the same order in which you removed them.
This would be a very good, and easy, time to install new drive belts. Replacing Maytag drive belts is probably the easiest repair in the history of appliances. Get a pair for the Helical drive transmission, not the newer Orbital drive used from the mid 1980s on. Belts are plentiful and not too expensive. Use only genuine Maytag brand belts because they are specially made to act as a clutch. If you do not use Maytag brand belts, they will not work as a clutch and the motor will overheat. This is essential on the transmission drive, but I do not know if the pump belt also acts as a clutch.
There are a few older models of Maytag that have the same guts as the later (up to mid 1980s) models, BUT are designed to be serviced from behind, rather than from the front. If your machine is one of these, your pump and motor will not be on the front of the washer, but the parts (pump, belts, etc.) are the same.
Please post a photo of your washer so we can confirm what type it is and offer you the most accurate advice possible. Whatever is wrong, it is definitely worth fixing. This washer is at least 40 years old and even with that many years of use, will still outlast a new one.
Best of luck,
Dave