Dishwasher slowly fills with water after use
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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