First off there is supposed to be no possible way to open the door while running. I would think that something in that circuit that you can't repair so that it is repaired the proper way, I will get to searching for you.
Microwave ovens store a dangerous electric charge - a capacitor is typically used. If a microwave hasn't been left off for many hours, without it discharging, the charge can burn or kill you, so it is not a recommended do it yourself repair. The fuses can be purchased and replaced easily, and I have done it on several occasions, but the danger should not be underestimated - trained technicians even can be hurt if they make a mistake. I regret having tried to do it myself without knowing how to be safe.
There is a door sensor in the door frame of your microwave that tells the microwave if the door is open or shut. That sensor is not working for some reason. The sensor is near the latch mechanism and is made of plastic and has probably broken and needs to be replaced. I would take it to a small appliance repair shop. Microwaves are nothing to fool with if you do not know what you are doing.
I suppose it is possible you pressed the wrong button - if you disconnect it from the power for a few minutes it should cancel whatever action you might have taken, though realistically it is more likely your microwave has developed a fault that is best tackled by the repair shop.