Now that it has cooled off, try holding the light switch button down at the door while setting the control to clean or cancelling the cyle if it is still showing self-clean. The door latch mechanism may be permanently damaged. The lock assembly is made up of a latch at the door which is connected to a long rod that runs to the back side of the range. The lock motor and switches will be found back there. For the stove not to work means that the lock assembly has stopped while the switches were disconnected during clean.
Tell your wife that self clean ovens are supposed to burn away the residue...that's how they work. Flare-ups are perfectly normal and harmless.
Door latch replacement is covered on page 81 of the following manual:Frigidaire Ranges
Or you can watch a video of the procedure:Lock Replacement