Washer won't agitate on wash cycle. Used to agitate just a little, now it's not doing anything. On spin cycle it appears to spin slower than normal and after the spin cycle has finished clothes remain somewhat saturated with water. Is this something I can fix myself and what part (s) need to be replaced?

HI Rhonda.
If your washer pumps out the water but doesn't spin, check these: The lid switch may be defective. ... The switch is inside the washing machine main housing near the door frame. Often you have to raise or open the top or front of the washing machine to get to the switch.4 May 2012

SOLVED: Why won't my Washing Machine pump but not spin during ...

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What causes a washing machine not to spin?If your washer fills with water but doesn't agitate, the problem is likely to be a faulty lid switch, a broken belt, or a problem with the motor. (Note: Direct-drive washing machines do not have belts.) ... 1Check the washing machine's spin cycle. If this works, the motor is operating and the belt is not broken.14 Aug 2014Washer Doesn't Agitate or Spin - HomeTipshttps://www.hometips.com/repair-fix/washing-machine-agitate-spin.htmlSearch for: What causes a washing machine not to spin?
Why is my washer not spinning the water out?If the washer won't drain there might be a clogged pump or hose. It's common for small socks or other small clothing items to get into the water drain system and clog the hose leading to the pump or the pump itself. Remove the hoses from the pump in order to remove the article of clothing.16 Mar 2014SOLVED: Why won't my washer spin or drain? - Kenmore 110 Series ...https://www.ifixit.com/Answers/View/.../Why+won%27t+my+washer+spin+or+drainSearch for: Why is my washer not spinning the water out?
What causes a washer not to spin?Over time, the repeated friction of the clutch pads rubbing against the housing can cause the clutch to wear and create a scraping sound. A worn clutch can prevent yourwashing machine from spinning, or may cause a slower spin speed which will leave your clothes wet after a cycle.How to Fix Washer That Won't Spin ' Washing Machine Repairhttps://www.partselect.com/Repair/Washer/Will-Not-Spin/Search for: What causes a washer not to spin?
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I would suggest checking ur cam dogs or coupler in the agitator, also the drive block and agitator spline and spindle as well. see pics

Sounds normal. Most machines do spit out a little water, rinse for a moment to loosen any trapped soap before they drain and spin.

I just encountered the same problem. I think the operation of the machine is such that the motor turns one direction for the spin cycle, and the other direction for the agitate cycle. I am replacing my motor, as I think i have a bad winding on the reverse. I will let you know.

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

wont drain

Not sure what you mean? if you have normal wash action then it is agitating in the wash cycle.  Otherwise if it doesn't agitate or spin but does fill with water then your motor or motor control board is bad.

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.