I seem to hear more often of these type of events where the engine turns over, but doesn't crank, on cars with pooooosh-button starters. Not just Mirage (this is the first I have possibly heard of such a case in a Mirage). But, for instance, seems my Lexus LS does similar things. The Lexus has a pooooosh-button start. And not only does it go through 50 million checks the instant the button is poooooshed, but I think the ECU looks for an engine rpm as one of the checks. Such rpm is based on the starter motor turning the engine. If it doesn't see the rpm it expects, it doesn't do something else (I can only guess) like firing fuel injectors. I speculate, but maybe that's what's going on with anjenorden's vehicle.
If you have access to a battery charger, let it charge up overnight, and see if it fires up the next morning. If it does, then that is likely proof that it is a weak battery. That's just a suggestion to *try* before replacing the battery. Charging up a 6 year old battery will only limp it along. Said battery still needs replacement (if in fact that is the root cause). However, if you are on a 5 or 6 year old battery, it wouldn't hurt to just go ahead and replace it in any event.
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View my fuel log 2020 Mirage ES 1.2 manual: 42.4 mpg (US) ... 18.0 km/L ... 5.5 L/100 km ... 51.0 mpg (Imp)