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Ok. The engine management light should come on when the ignition is switched on and stay illuminated until a couple of seconds after you start the car as it needs to do a system check after starting to make sure all the sensors are getting the right readings. It should then go off and stay off unless the ecu picks up a fault somewhere and so then comes on to warn you that there is a problem.
Unless you have access to a code reader then unfortunately what you are going to have to do is take the car to a different garage and get the car plugged in again and get them to read the faults. It does seem that the light has been disengaged somehow.
If you do have access to a code reader, what you can do is read the codes stored on the ecu and then unplug a sensor on the engine and then start it up and drive it a short distance and then plug the code reader back in and see if another fault has logged even without the light coming on. This will then show that the light has been disengaged.
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