Computer won't detect any issues with my car?

My Ford Fiesta zetec 2003 shows a yellow engine management light in ignition mode. But it's been there for almost And I've not really bothered with it as my vehicle had no issues.

But Recently from 3 weeks my car constantly turns off when I release the accelerator to slow down or stop while driving. For example at the traffic lights, approaching a roundabout, turning from a road. The engine just dies on me and goes into ignition mode. However, i have no issues while driving & accelerating, not sure if it's connected to the engine light but I took it to a local garage, they said no faults seem to show when they connect my car to the computer so they can't fix it. I don't understand what I'm supposed to do now, because there's definitely something wrong with it.

What program or scanner were they using? If the light is on there must be a fault.
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Then do a tune up, clean the throttle body, and check to make sue the timing belt hasn't jumped out of time a tooth or two.

Probably the engine runs very low on oil or the oil is to old and so very worn out that it has become like resin on the engine parts.

Dealership

Obviously you need to find a better mechanic. Or at least someone that knows how to repair vehicles. My first guess would be worn out engine.

You need to take it to someone with the correct diagnostic code-reader - if the engine light is on there will be a stored fault code.

You should have had the fault investigated as soon as the light illuminated - driving with a fault may have caused further damage.

If the car cuts out when the accelerator is released, I would suspect a fault with the idle air control valve, assuming it is a petrol car. However I would not replace anything until you have found and translated the error code that is causing the light to illuminate.