So nothing at all happens when you try to start it? Try starting it in spin and see if there's any life there.

This is going to be a tough one to diagnose I think.
In any normal cycle I'd expect it to fill before it tries to turn the agitator.

Unplug the machine. There are 2 screws at the bottom of the front panel, remove them and the panel will slide down and come off. Look for any obvious corroded wires, copper turns green when exposed to water and can degrade quickly. The moisture can corrode contacts in the timer and other switches that didn't actually get wet.

I know you say that power is ok at the outlet but I'd have to start at the beginning. I've had many customers say the power supply was ok when it wasn't. No reflection on your abilities but that's just where you start.

So if a quick check didn't reveal anything my process would be to verify 120v at the outlet, between the two vertical terminals. If there than verify that there is 120v inside the control area; between black and white I think.