Samantha, that clutch switch interlocks the starter, not the fuel or spark. Same for an automatic, there's a neutral-safety switch that prevents starting in gear.

But either of those cases, the starter doesn't crank the engine. Cmthomp2 says the starter turns over the engine in his case.

 

Thanks everybody for the suggestions. Honda dealership in town diagnosed it as a faulty pcm. Been running fine ever since.