I have a Kenmore Ultra Wash 665 15817990 and was having similar issues....washer wouldn't start, and lock light would stay lit and/or flash. I had been able to kill the power for some time, reset the machine, and get it to wash once but it didn't sound very happy about it. This last time that trick didn't work, and some of the other wash cycle lights appeared to be dimly lit.
Using the answers here, I took all the screws off the inner door panel, removed the black plastic cover, and one-by-one pulled each electrical connection off the control panel. I used quick drying electrical contact cleaner sprayed into the socket end of the wiring harness to (hopefully) remove any dirt preventing a good connection. Inadvertently, I did this with the circuit breaker turned ON (!), although I would not recommend this. :) I flipped the breaker back to off, reinstalled the black protective cover, reinstalled the inner door, and left the door open. I flipped the breaker, closed the door (no dim lights - good sign!), pressed the normal wash button, and hit start. VOILA - SHE WORKS! It's still running now, so we'll see if it makes a complete cycle, but I'm hoping for the best. Even if it's not a permanent fix, it's not too tough to do and will buy me some time till our kitchen remodel in the next couple of years. We're replacing all the appliances at that point and I really wanted to avoid buying something to tide us over till then. Fingers crossed and knocking on wood this keeps on tickin'!