There are plenty of things that can cause this, but being a petrol engine with no turbocharger, it shouldn’t be too tricky to diagnose. Any time an engine runs well when warm but struggles when cold, suspicions are drawn to the fuel/air mixture. A warm engine needs a very different mixture to a cold engine, so modern engines have sensors that monitor the engine temperature, the air/fuel ratio and how well that mixture is burning. If any of those sensors are not telling the computer everything it needs to know, poor running can be the result.

But it would also be worth looking at the air intake side of things. An air or vacuum leak into the intake manifold can also cause rough running and hard starting. The engine’s stepper motor (which controls the idle speed) could also be at fault, but could also be the victim of one of those non-working sensors.

First things first; have the car electronically scanned to see what fault codes are thrown up. From there you can make a much more accurate diagnosis of the problem. Simply replacing random sensors and other parts on a hunch is a fast way to throw money away and still be stuck with a car that doesn’t run properly.

The de-carbonising process you mention is sometimes necessary in modern turbo-diesels which, for reasons of emissions control, consume a percentage of their own exhaust gasses as well as any gas build-up inside the actual engine. And since the exhaust gasses contain soot, and the crankcase gasses contain oil, those two compounds get mixed up into a black, gooey paste that clogs the engine’s intake system. At this point it usually needs to be pulled apart and manually cleaned. If this is the case with your car, it could well be the cause of the check-engine light and the poor running.

This is possibly a fault with the smart key which not only physically unlocks the car, but also disables the immobiliser and allows the car to start. Have you somehow managed to lock the keys in the car at any stage and retrieved them with the spare key? If so, try the spare key to see if that will now start the car.

I’m told that locking the keys inside the car and opening it with the spare key, will wipe the electronic coding on the first key, meaning that it will no longer unlock all the electronic security measures. You can take the key to a dealership and have it recoded. Perhaps it’s just that the key has failed electronically for no good reason and needs either a new battery or a new key module. Generally speaking, messages like `No VID Found’ suggest that the key is not talking to the car’s body computer. Often it’s the key, but sometimes it can be the body computer itself.