Here are your parts.
As you can see there are several that match yout unit so I chose KUDS25FKPA1.
Replacement parts for KUDS01FK models | AppliancePartsPros.com

See the attachment for the tech sheet.

First have you disconnected/removed power (flip the breaker) from the unit for a few minutes to see if it will reset.

The normal way to troubleshoot is to disconnect the keypad at the control board and check the key outputs with a meter. If they check out OK then replace the control board. Still a bit of a crap shoot but your odds of getting the correct part are better.

As you can see the keys share a line/track with other keys so if the other keys using that line do not work then odds are it is a keypad problem.
Note: that the unit uses a separate ribbon cable to connect the boards so it may be the problem. This is checked with a meter to be sure all lines/tracks are 0 ohms.

If your investigation points to a key not closing I would try the following first unless of course you narrow it down to an actual key not closing.
Connector Cleaning / Checking
Unplug the unit
Open it up
Remove the ribbon cable from the keypad to the control board at the control board.
Clean the edge connector.
If it is the type where there is not a connector just the insulation is removed, it can be cleaned with a pencil eraser. Do not use an ink eraser as it is too abrasive.
Check the tracks in the ribbon cable for hairline cracks. A magnifying glass helps here.
Would not hurt to clean the connector on the board. Use electronics contact cleaner or isopropyl alcohol and a tooth brush. Be gentle and do not reconnect till all the solvent evaporates.
Reconnect everything and give it a try.

I am experiencing the same problem and have started a thread, but wanted to ask what the update is with your situation regarding the ribbon cable. I have replaced the control panel (with the new button membrane) and all the other buttons light up except the start LEDs --- thanks!

Yes, I have been "fixing" mine for about 2 wks now because I refuse to pay someone a large chunk of money that I may (or should) be putting towards a replacement :) .

My dishwasher is a different model number than yours - KUDP01FLSS6 - a kitchenaid superbra that came with the house when we bought it - BUT, I believe the buttons and mechanisms operate in the same manner ; the acutal aesthetics/location of buttons it might be different.

On my model there is a distinction between the "Control Panel" and the "Control Board/User Interface Board". I have purchased and installed the Control Panel which is just a plastic shell that has the replacement membrane that goes over the buttons (I noticed that there was a crack in the membrane over the "start" button when the problem was discovered - that piece of plastic was approx $75). I was hoping that by basically replacing the membranes over the buttons would solve the problem; it didn't (check my thread for a detailed description of additional checks I did).

Yesterday I went ahead and ordered a NEW "Control Board/User Interface" which looks like a green "mother board" computerized piece with the buttons attached to it, because the only problem appears to be that the "start" button doesn't cause the "wash" and/or "option" button I select to blink once more after the "start" button is pressed to indicate to me that the signal was received. (I hope this makes sense) (and that crack in the membrane on the control panel that covers these buttons, was over the start button). I was able to find NEW "control board/user interface" on the net for approx. $122 and I will be refunded $35 when I return my "bad" "control board/user interface" to them. So if this works out - I will have spent, well approx $100 +- on this part (due to ship. costs). It arrives tomorrow. I will update you on whether this, indeed, solved by problem and tell you at least what my part numbers are.

Side Note: For me, if this doesn't solve my problem, I am fortunate enough to be able to return both parts purchased for a full refund less shipping. I will then likely investigate if it could possibly be the other "control board" that connects to the interface panel - but there appears to be continuity with the heater elements and fuses therein, so.....it I may think about a new dishwasher because I believe if I had called a tech. out here - it would cost me approx $300-400 and as I said, I have already checked about 95% of the sensors and switches (the dishwasher is 6 yrs old and is run 1 or more times a day). Will let you know and would like to continue to hear about your progress as well. Good Luck.

Carolyn, so glad you got your dishwasher working. I haven't had such success. I actually got mine working for a couple days (trying different things) but then it went out completely. As in no power at all, none of the leds light up on any button. I will need to investigate further. I will also look around for better pricing for the control panel... I don't want to spend $230 to repair such an old dishwasher. Maybe you could share the website you bought from? (or maybe that's not allowed here :)??) Seriously, very glad you got yours working... job well done.