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So your issue is with the door latch. GE oven door latches fail more than any other oven I know. I understand the door isn't locked shut, but the sensor on the latch that tells the board that the latch is in the open position isn't working. You can try to start self clean and cancel it after 60 seconds to see if the latch will reset, but if it won't stop flashing the signal on the display, the latch will need to be replaced before you can use the oven again I'm sorry to say.
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Whether the door opens or not, unfortunately the door latch has failed. Holding 9&0 doesn't lock or unlock the door, that is for a control lock to prevent you from using any buttons on the touchpad (like a child safety lock). If you've already jiggled the latch and reset the circuit breaker, the only thing you can do is replace the door latch because it's not sending the right signal to the control board or it's stuck somewhere between the open and closed position. Either way, the latch assembly would need to be replaced to resolve this issue I'm sorry to say.
Hello again. I'm just following up because I haven't heard back from you and I see this question is still open. Is there anything else I can help you with?