When you say you can't get the water to drain, is the washer attempting a spin cycle? These machines have reversing motors, so during agitation the motor turns one way, then during spin it turns the other way. The duration of the spin cycle is controlled by the timer, so if the motor isn't reversing the washer would appear to do nothing for a spell as the timer continued to advance until the spin time was used up. Then since the water hadn't drained out the fill level selector switch contacts would still be closed and the timer would continue on with the rinse cycle agitation.

The plastic Maytag pumps are pretty bullet proof so it's hard to imagine one seizing up unless some foreign object got inside and jammed it. Also noteworthy is that pump is in constant motion during agitation and spin. If it truly is seized up you would likely smell and hear something as the belt is dragged across the stationary pulley - that is unless the belt is missing altogether. I suppose that's also worth looking into.

How many hours should it take a professional to R&R the pump?  $200 seems like a lot for labor.

Here in The DC Area we would charge $72 for the Service Call, $22 for 15 minutes of labor and $42 for a new water pump and $20 for a used one with a one year warranty on parts and labor.

Often big cities are the least expensive places to buy things or get them fixed.

If your agitator has no set screw on the side of the barrel then you remove it by pulling it straight up. There is a rubber stop ring mounted below the splines on the steel shaft that the agitator sits on and that is generally all that holds it in place. The stop ring has a slightly larger diameter than the bottom of the agitator so you'll need to pull up firmly to get it to compress enough to let the agitator slip past. Unfortunately, depending on how old the stop ring is it may have hardened up a bit with age making this potentially very difficult.

As to the little hole in the agitators skirt that you mentioned, by design the agitator will trap an air pocket underneath it as the tub fills with water. That little hole simply allows some of the air to bleed out so that the air pocket is no larger than needed.

Hi the washers with a screw to hold the agitator in place do not use a rubber O ring.

Maytag went to the screw to hold the agitator in place because the older machines that only used a rubber O ring the agitators would occasionally fly off the post during the spin cycle and cause injury or other washer damage.