Water fills to proper level but agitator doesn't come on instead there is a grinding noise, when I move control to just prior to rinse cycle water drains properly, but still just grinding or buzzing n

probably you've got something blocking the water pump from doing its job properly so check that the water pump is free running emptying all the water if not then there is a blockage in the pump normally ist a button, paper clip or other debris out of a trouser pocket eric

The typical cycle is;
fills to selected water level
agitates wash cycle
drains wash water
spins wash cycle
fills to selected water level on rinse cycle
agitates on rinse cycle
drains rinse water
spins final time
end of cycle

if it's a top-loader, then the water level sensor is probably failed! if an older machine- there's a plastic tube (which you can't see from the outside) that measures the column of water in the tub of your machine, and triggers the agitate and spin, and rinse cycles of your machine.
when it's in wash cycle the water level is lower, then it spins and drains and the rinse cycle pumps in more water (makes sense!), then drains & spins, then re-rinses at the same water level. your water level sensor is defective, probably. allowing it to over-fill.
it detects the water level as 'spin' and doesn't agitate!
my theory- no guaranty! if it's old get a new washer or a good used one! this is not a problem i've encountered, just a guess. good luck!

There may actually be more than one setting on the diaphragm control, or you may two diaphragms each with their own setting control. I hope this helps you! Good luck!

the entire agitator is not moving during the wash??? or just the top section that looks like a big plastic corkscrew???
or is the unit actually just filling with water, making the motor running noises and going thru the motions of running a cycle yet not actually moving anything within the unit, then draining out as normal??
if just the top section of the agitator is free spinning instead of ratcheting as normal you'll need to replace the agitator dogs if present.
if however the units just filling and draining of water with no inner movement then more likely the drive coupling is bad and needs replacement..
hope this helps,
best of luck,
ttfn

you need to replace the water level switch

same problem

I was partially wrong on my diagnosis. No cold water enters on either the wash or the rinse cycles. I also heard odd noises from the inlet valves. I realized the cold water valve was not opening. I've ordered the mixing valve and plan to replace it as soon as it comes in.

Your air pressure hose going to the water level switch is pinched.
Open the top control panel to access the clear plastic tube and relieve the pinched area.

is it possible that the washer was overloaded? if so the agitator has little plastic "gears" that move the agitator one way only, they could have made the sound. 
you can also check under the washer to see if anything (like a coat-hanger or something) is interfering with moving parts of the washer