All 4 buttons are blinking and then the machine switches off

Isn't there a button you hold in until oil pressure recovers when starting, the button is usually next to the starter switch.

Just a brief addition, I don't have the Magimix model, but I have a similar one. It loses it's programmed settings if it is unplugged or switched off at the wall, but if you leave it plugged in but turn it off with the switch at the back it keeps the settings you have put in. It draws virtually no power when it's switched off with the switch on the machine, (I checked it with a power meter).
Just thought I'd share that with you.

power off the machine using main power switch not the control panel switch

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Door lock faulty probably,,,,try closing door,,switching on and lightly thumping door near handle

pe error on the machine is normally the pause in action. try pressing the start /pause button again to activate the wash program

Those blinks [flashes] are fault indication (Error Codes). From the number of blinks occur at one time switch ON, you can get an idea about the faulty circuit section inside it. This will make repair easy. These are called blinking codes. Make sure about the exact number of blinking of the standby/power LED, by switching On & OFF the set, for at least two times. Count it carefully. If you wish to get some details, check the site linked here. It has details about blinking codes, and fault locating procedure, to many popular brand TVs and other devices.
http://electro-medical.blogspot.com/
http://homenol.blogspot.com/
http://electronicshelponline.blogspot.com/
If blinks continue without any pause, the main board is faulty.

The power button blinks when it is heating the water up prior to use. It should switch off automatically when the water has boiled.

I had a similar problem where both Small and Large cup buttons on mine blinked intermittently. I did a reset of the large and small cup flow levels based on the following and it seems to work fine now:
1. Switch off power 2. Press and hold Large cup button 3. Switch on power while still holding down large cup button
See if that solves your problem.

small set of gears in the service section (cartride cleaning section ) is broken