However, that is not a guarantee that the engine can't start. Apart from the obvious issue of a potentially broken ground wire, it is also possible with some keys, to remove them from the ignition switch, when it is set to Both.
If this happens then the mag switch is US and the aircraft
must be grounded until it is fixed. All of the standard light airplane mag switches are specifically designed so that you can only remove the key when the switch is in the off position.
I check for this at the end of every flight by giving the key a little tug at each mag position as I cycle it to off. I have found a few bad switches over the years, all in high time trainers where the switch is just worn out. My guess is in all cases the switches had been like that for awhile but nobody had paid any attention to what they were doing when they shut down