Fuel (delivery)/ignition systems.
Dirty injectors, damaged or clogged fuel rails, blown high-pressure hose, worn gas lines, distributor, alternator, coil
, spark plugs, starter motor, fuel pump. Any of those. It doesn't seem too likely that humidity is making that much of a difference, especially if your coil is the issue, but I suppose ionized (post-thunderstorm) air could have an effect if the charge is weak enough.
And, of course, there's always the battery and its connectors. More knowledgable members might be able to help you out more with a better description of the problem.