Here are your parts
Replacement parts for WHIRLPOOL KEBC207KSS05 | AppliancePartsPros.com

Here is the parts breakdown
http://www.servicematters.com/d...0Sheet%20-%208302066.pdf

You will notice that the control board has a thermal fuse in it's power supply connection. I could not find this in the parts breakdown perhaps you will have better luck. This may even be built into the wire (with a piece of heat shrink over it) that goes from P19-1 to L1.
Remove power from the unit and check this line for continuity Should be 0 ohms. Remember to disconnect one side of the wire to ensure that you do not read an alternate/parallel circuit path.

I would check that you have the correct power going to the unit 240 volts from L1 to L2 and 120 volts L1 to Neutral also L2 to Neutral.
Note that the board's power supply gets power from L1 to Neutral (120volts). Sometimes you can loose Neutral without actually tripping the breaker.

Check that the secondary of the power transformer is 23 volts AC.

Another thing to try is to disconnect the keypad and try it usually the control will at least light up something with the keypad disconnected

Be careful 240 volts is lethal.

One thing that I did notice is that the transformer is showing nothing acrross the Line terminals and 2.2 Ohms across the load terminals.
Then I would say that you problem is here, you should see continuity across the transformers line terminals.

PS: I also noticed i mislabeled the second link, it should be a tech sheet, guess I should have had another cup of coffee before getting on-line.

Glad you found it.
You are a better tech than the plug and chug jockey who replaced the control board.