This may have been induction icing or carb icing. Incorrect leaning. Three adults and fuel in a PA28 and you’re close to weight limits.
At a density altitude of 9000’ the rate of climb is below 500ft/min. Even just a whiff of a downdraft puts you in a decent.
Maybe lost a magneto hence the starting issues.
She saved her passengers and let’s be gentle judging the inexperienced.
There’s an appropriate saying about a bucket of luck and bucket of experience.