My Maytag washing machine will fill with water but will not agitate as soon as the water level gets up the water shuts off and when it shut start all that happens is that it makes a humming noise

Does it fill with water to the correct level? The water pressure switch lets the machine fill to a certain level and the stops the water coming in, then the control board should start the agitation.

The first video might help you.

https://www.google.com/search?q=Maytag+Centennial.+It+starts+to+agitate+while+the+water+fills+in+the+beginning+of+the+cycle

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Usually a top loader will not agitate until the fill sensor is satisfied. If the water has shut off, and is up at the desired level, the fill sensor has done part of it's job. Check the connections there, and at the timer. It may just be a loose connection.

Cut off switch to water valve or sticking water valve, does it do it on both hot and cold water settings?

The water-level switch regulates your washer's fill volume. This switch is usually a diaphragm device with a small, clear tube attached between the switch and the bottom of the washer's outer tub. As the water level in the tub increases, the pressure on the air in the tube increases. When the pressure reaches a certain level, it activates the switch, shuts off the water, and signals the timer to begin the agitate cycle. If the switch is defective, it may prematurely signal the water to shut off. If so, you probably need to replace the water-level switch.

If the washer makes a humming sound, but no water goes in, and there is no other action, the water shut-off valve is off (outside the washer), or the pipes are frozen.

For top-load washers: If the washer starts agitating immediately without filling the tub, the water level switch is bad (falsely senses the tub is full already) or the water level sensing hose plugged up while there was water in the machine, and it has still has pressure inside it to fool the level switch.

A common problem with noises from washing machines has been the under wire that may come out of small clothes. In the washer they can get stuck in one of the inner basket holes and make a scrapping noise, they can actually make there way into the pump and jam the pump, or make a terrible noise when the pump is running. Grab a flash light and have a peek inside the washer for this. Front load washers seem very common to this happen! If the tiny cloth  is showing signs of fraying, may be best not to wash it in the washing machine, replace the cloth.


Maytag Dependable care washer.....Locate a 1/4 inch screw on the side of the agitator, ( about 3/4 of the way down) remove this screw and lift up on the agitator...picture.
 
Maytag Atlantis, Norge, Performa by Maytag.....Remove the cap and softener dispenser by pulling it off and locate the agitator bolt, remove bolt and lift up on the agitator...picture.


Water level controls - The water level control is also know as a pressure switch, this is where you set the water level ( small - medium - large ). The water level control is responsible to shut off the power to the fill valve and direct that power to the timer so the washing machine can start up. The WLC has electrical contacts in it that sends power to the fill valve and when the WLC is satisfied the water level is correct the electrical contacts open power to the fill valve and send the power to the timer and the washer starts. Picture of this here. How the water level control knows when it is time to shut the water off is, a air tight hose runs from the outer washer tank to the water level control. As the water fills the outer tank air is pushed up the hose, depending on which setting you have made ( small- medium - large ) is takes a certain amount of this pressure to make the WLC cycle over and shut off the water and send this power to the timer. If this hose develops a leak or a pin hole the washer can over fill as the WLC may not be able to shut the water off. The water level control can also break down and allow the washer to over fill as well.
Testing a  water level control or a fill valve can be done by using a Testing a  water level control or a fill valve can be done by using a ohm meter or a volt meter. Testing a  water level control or a fill valve can be done by using a ohm meter or a volt meter. Testing a  water level control or a fill valve can be done by using a ohm meter or a volt meter.
A couple of tips from readers (Thankx!! ):
~ If you have a loose hose on the water level control or tank end, use a plastic wire tie to help hold the hose tighter and make a tight fit.
~ The water level tube (tube that runs from the square box), access panel on the outer drum where the bleach tube also ends) from the pressure sensor switch (front panel) can become clogged.  Or the two holes from the outer tub into this square box panel on the outside of the outer tub can become clogged. Either clog, I am told by my help repair guy can cause the sensor to think that there is still too much water in the tub and so will not allow motor to activate spin.
~ If the water level control contact is bad, it may also stop the filling ok, but not tell the washer to start agitating.
 

Water level controls - The water level control is also know as a pressure switch, this is where you set the water level ( small - medium - large ). The water level control is responsible to shut off the power to the fill valve and direct that power to the timer so the washing machine can start up. The WLC has electrical contacts in it that sends power to the fill valve and when the WLC is satisfied the water level is correct the electrical contacts open power to the fill valve and send the power to the timer and the washer starts. Picture of this here. How the water level control knows when it is time to shut the water off is, a air tight hose runs from the outer washer tank to the water level control. As the water fills the outer tank air is pushed up the hose, depending on which setting you have made ( small- medium - large ) is takes a certain amount of this pressure to make the WLC cycle over and shut off the water and send this power to the timer. If this hose develops a leak or a pin hole the washer can over fill as the WLC may not be able to shut the water off. The water level control can also break down and allow the washer to over fill as well.
Testing a  water level control or a fill valve can be done by using a Testing a  water level control or a fill valve can be done by using a ohm meter or a volt meter. Testing a  water level control or a fill valve can be done by using a ohm meter or a volt meter. Testing a  water level control or a fill valve can be done by using a ohm meter or a volt meter.
A couple of tips from readers (Thankx!! ):
~ If you have a loose hose on the water level control or tank end, use a plastic wire tie to help hold the hose tighter and make a tight fit.
~ The water level tube (tube that runs from the square box), access panel on the outer drum where the bleach tube also ends) from the pressure sensor switch (front panel) can become clogged.  Or the two holes from the outer tub into this square box panel on the outside of the outer tub can become clogged. Either clog, I am told by my help repair guy can cause the sensor to think that there is still too much water in the tub and so will not allow motor to activate spin.
~ If the water level control contact is bad, it may also stop the filling ok, but not tell the washer to start agitating.


Maytag Dependable care washer.....Locate a 1/4 inch screw on the side of the agitator, ( about 3/4 of the way down) remove this screw and lift up on the agitator...picture.
 
Maytag Atlantis, Norge, Performa by Maytag.....Remove the cap and softener dispenser by pulling it off and locate the agitator bolt, remove bolt and lift up on the agitator...picture.

 

In yor machine control panel you have A part called a pressure switch or water level switch. that controls the water level and tells the timer to start aggitating .If the part is bad the machine will over fill and keep running the water!!

How do you get it stop filling? If it stops filling by just shutting the timer off you may have a bad pressure/water level switch, if you have too shut the water off too the machine at the wall then you have a bad inlet water valve.

First thing to check is the filter,
DISCONNECT power
open the bottom pane (3 screws on bottom front lip)
in the cent is a large removable filter ,
set a pan or rags under it ,there will be water.
clean out any debris an be sure the pump impellers move freely.
let me know if that fixes it.