OK. Not a professional, but I happen to have a lot of experience with this situation. For reference, I have a Whirlpool RBD305PDT11 Double-Oven with a "Self-Clean" feature.
Inevitably, my bride decided that she would "clean" the oven. She set the controls and let it go. At the end of this procedure, I noticed that the electronic control board no longer showed the time or any other lights. So, I checked it out and found that the oven was ENTIRELY non-functional. Virtually nothing would work.
Since this oven is hard-wired, I turned off the fuse and let it sit for few minutes (these things are just computers, so I thought that I would "reboot" the whole thing). This did nothing.
Then, with the help of the internet (thank you, "Fixya"), I found out that this model of Whirlpool oven (and many others of different brand names) seems to have this sort of problem all the time.
It turns out that the physical act of using the "Self-Clean" feature, with its very high heat, blows a few "Thermal Fuses" that are one-use only and cannot be reset. They must be replaced.
First, be sure to turn off the power to the oven BEFORE doing anything. I did this and then took the oven out of the wall enclosure so I could get to the back of the unit. For sake of brevity, I will not go over the procedure to take the oven out of the wall, but those instructions can be found on the internet. Several metal screws hold the sheet metal covering on the top and bottom. Note: This has happened to me twice now (my bride used the "Self Clean" feature without my knowledge) and I have found that the lower Thermal Fuse has NOT blown either time, but the top one has blown both times.
On this unit, the "Oven Shutdown Thermal Fuse" (part number 4451442 costing about $40) is attached with two screws and is located on the upper left section (picture attached below). It is very easy to take the two wire leads off and remove the two screws holding it in place. You can then check this item with a Multimeter to see if the fuse is working. I won't go over the Multimeter instructions, but, you are looking for "Continuity". If you have continuity (electricity will flow), the fuse is good. If you do not have continuity, the fuse is bad.
The first time that this happened (about 5 years ago), the control panel still had lights on and was issuing "error codes" specific to this brand of oven (I don't remember the codes...F1 or something) and the only problem was the fuse as discussed above.
However, the second time that this happened, as I mentioned earlier, the control panel was blank also. So, I had to look for the "Control Panel Thermal Fuse" also. This fuse can be accessed from the FRONT and is behind the control panel. In this unit, that part number is 4451042 and costs about $20. This item is sheathed in clear plastic with a "bullet-looking" thing inside of the plastic. It is very easy to pull this fuse out and check it for continuity to see if it is in working order. Continuity (electricity can flow from one side to the other), and the fuse is good. No continuity, and the fuse is bad. Again, you can check the continuity with a Multimeter. In the second instance of this happening, this fuse was bad also (that is why the control panel had no lights or error codes or anything).
Once I replaced these fuses, the control panel came back, the oven would then respond and worked just fine. If I was to guess, I would say that the cabinet that the oven is installed into is too tight of a space and the temperature just gets way too hot and the fuses blow. This is just a thought, but maybe a fan set to blow at the unit when attempting the cleaning process would help keep the unit somewhat cooler on the outside. But then, at $60 to fix and all of the hassle involved, I am NOT willing try this just to see if it helps!
Just to get in a rant....How a company can sell a unit with a feature of "Self Cleaning" that, when used exactly per the instructions, will render the unit completely useless is WAY beyond me.