The washer will not fill or even give a sign that it is starting but will operate in the spin cycle.

The washer will add water in the rinse/pin cycle even while it is pumping out. This is to give the clothes a wash while spinning to remove excess soap suds. Could this be your problem

not sure but it sound like the timer

Remove the front panel and check for a broken belt.

its suppose to start with lid down,the draining may be a faulty water level switch so this needs replaced.

Blockage (small) at drain filter?

Check the water pressure switch for proper operation

it will fill but won,t spin, will throw out water as if it washed, then it take water to rinse but won,t spin ,then will throw out water as if it did , but clothes are soaked

if this is a frigidaire as in the healine , then see if the tub turns over at all. if not then it may be the inverter board located on the bottom right rear. If there is water left in the tub now that water should drain before it will fill again. check drain pump for obstruction/operation.
for the inverter, there is a techsheet in the bottom attached to the wall, It gives info for checking it. Have a multimeter handy.

A defective pressure switch can interfere with the cycles that depend upon the switch to indicate when water has filled or emptied from the tub. It can also result in underfilling or overfilling of the tub. The switch routes current from the timer control to the temperature switch and the water inlet valve when the tub needs to be filled. Once full, the pressure switch cuts the current and reroutes it to the motor on the timer control to continue the cycle.

Well, it sounds like you've done your homework. My first suspect would have been the agitator dogs too, but you said they were fine. Another likely suspect would have been the motor coupler, but you said the washer spins during the spin cycle. If the coupler was bad the unit would fill, but wouldn't agitate or spin. Plus, it would make an awful noise. I would have also suspected a clutch assembly, but you said the wash tub can spin. Normally, when the clutch goes bad, the drum won't spin, or spins slow. Another suspect could have been a bad lid switch, but the washer would have filled and stopped, without agitating or spinning. The only remaining suspect that I'm aware of is the gear case (transmission). Checking under the washer can give you some clues. Normally, when a gear case starts to go bad, they leak an amber colored oil. You may find puddles or drips under the washer. If you see no signs of oil the gear case could still be defective, however. But, before you go through all the trouble, double check the agitator one more time. Completely remove it from the tub and check the under side to ensure the grooves that grip the top of the gear case shaft have not been worn smooth. I hope this may have been some help to you.