I made two threads about this (now 24 year old) washer last year, first I had the coupler explode on me and then about a month later the motor controller went out. The second problem took me about a month to track down and fix, and the washer had been fine until tonight.

I was washing a load of towels and then I believe at some point during the rinse or spin cycle, it just crapped out on me. It will just sit there and do nothing, much like it did when the controller died. I don't believe it's the timer since I still heard it ticking away, but I do have a spare sitting around that I got last summer when I thought that might have been my problem.

I also don't think it's the controller itself since it shows no signs of damage or being burned out, the previous showed discoloration on the tips and the end of the wiring harness, but there's none of that this time around. It all looks clear and clean to me.

So I have the same issue as last year but none of the evidence to support it, what do you guys think it could be? Please help me because I'm at a total loss. And finally, the model number is KAWE540WWH2 serial number is CB2501219.

Have you checked the lid switch?

The motor and timer are no longer available.

So at this point the motor will not agitate or spin?
You are right in some models the lid switch does not defeat the agitate mode. So if it is not agitating nor spinning the capacitor might be the culprit.
Testing it is easy if your multimeter can test for micro-farads.
Yours should test between 189-227 µf (microfarads).
here is a video how to
https://www.youtube.com/watch?v=...Q&list=TLLho_Wu2HBHk

That is a crude way to test a capacitor however that way doesn't give definite results. It sounds as if it might be ok the only way to know for sure is to be able to test it's capacitance (farads) not just its resistance (ohms)
Since you do not have a digital multimeter perhaps a friend, neighbor or relative might have one to borrow.
In the mean time have you tried the spare timer?

I would recommend this one
https://www.lowes.com/pd/Southwi...ital-Multimeter/50125841
It has a setting for CAP (capacitance) that will automatically check for micro farads and nano farads.
The one you show only has a max setting for 20 µf micro farads and we need to be up between 189-227 µf.
The one I show also has an adapter to check temperature. I use this in my work to check the exhaust temp reading of dryers to see if they cycle between 155/165 to 125/135 degrees roughly. Lets me know if exhaust is clear and cycling thermostat is operating properly.