Receptacle – How to Safely Plug in Dishwasher and Water Filter to Same Outlet

My best guess is that the impeller has worn down enough that it no longer makes a good enough seal to act as a check valve. That's drain water seeping back in.

The dryer on a DW is that metal rod running along the bottom. The hole on the side is the fill inlet.

If it is fresh water leaking in, having replaced the valve the only thing left is the control board. The original purchase price, replacement cost and/or repair parts availability and their cost will dictate your economical options (don't buy a $100 control board for a $200 DW).

Replacing the impeller is a relatively cheap lets see if this works solution; replacing the control board would be of the this had better work kind.

Tracking this down may be more work than it's worth. It's not uncommon for most dishwashers to have some water remaining in them. If it's not spilling onto the floor or growing mold, who cares? If this was a friend-house-call, I'd tell you to (a) call me back when it starts leaking on the floor (b) buy an impeller kit (c) stop throwing money at it and buy a new one (the cost difference between new dishwashers is noise level; they all work just fine).

That is of course, after having insured that the drain line is elevated to reduce back-flow and that it is free from blockage by doing a garden hose enema with the impeller removed. If you're lucky, there's a grease plug fouling up the works.

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If your circuit breaker isn't tripping when the old or new dishwasher ran a full cycle, then hardwiring won't change a single thing. Check that your drain hose is clear & run up to above the sink trap or underside of the countertop.

There should be quite a forceful stream of water visible in the garbage disposal or sink drain. If not & you have an Air Gap atop the sink, then take the cap off the Air gap (dishwasher off) & clear all debris. You'll need to snake something down the hose leading into the garbage disposal or sink drain until you can see it come out in either. Correct any hose under the sink to be as inclined as possible above it's connection so future flow-back is eliminated.

And, especially check that the bottom of the dishwasher's inside grate or strainer is clear...if clear glass ever broke in there you really won't notice it blocking the water exit. Also, if you wash food product jars without completely removing labels, they will gum up the works quite badly & quickly.

All this should get you back in tip top shape. A new dishwasher doesn't fix an old or worsening clog.