It is very unusual that the oven control did not display any fault/error codes when it failed to go into the self clean cycle, or still operate in bake or convection. When you said that the door light came on, you mean the word "DOOR" came up in the display or the oven light came on? When the word "DOOR" came on and it beeped 3 times the word "LOCKED" did not display? The word "ON" also did not come on? It just went back to the time of day showing without the words "DOOR or LOCKED" displayed?
You will need to call a service technician to diagnose and repair your range. However you should be able to manually unlock the oven door by following these instructions.
NOTE: First, Unplug or disconnect power to the range by turning both breakers off dedicated for the range.
You will need to slide the range out and get behind it. Remove the panel behind the console and you may also need to remove the larger panel too below it. Remove all the screws to remove the panels. After your remove the panels your should be able to identify the locking motor assembly. The lock motor will have two black wires attached to it. You will also see three other wires (orange, brown and grey) connected to the door latch motor switches. You will see a long round rod connected at the lock motor and the other end connects to the door latching mechanism. The motor rotates the rod left and right to lock and unlock the door. Remove the two screws securing the lock motor to the rear of the range, then slide the assembly back to release it from the lock rod.
Rotate the rod after disengaging it from the locking motor. It will rotate left and right to lock and unlock the door.
The failure could be the locking motor, switch, oven sensor or control board. I recommend calling a service technician to diagnose and repair your range.