1998 Honda accord sometimes won't start

I'm not the car savy one in the house, my husband is but since he's working a lot I'm
trying to do what I can to help figure what it wrong with our Honda.  So I'm going to try to
explain this best I can.

It started as it wouldn't start. No clicks or anything.  All the proper lights would come on
etc.  when you turn the key nothing would happen.  Something would catch just right
though and it would start just fine.  Today it refused to start when he went to pick our kids
up from school.  He said it would click when he turned the key this time though.  He
considered it was the starter or the starter solenoid.  He eventually got it to start an hour
or so later.  But they way he got it to start made him think it might be some kind of switch
by the shifter. (Automatic) what he ended up doing was shifting it to neutral and see if
he'd be able to push it incase that was what he'd have to do to get it home from the
school.  When he realized he could, he went back put it back in park and just for giggles
tried the key again and it fired right up!  So he's wondering if there is something wrong
with the switch by the shifter.
Any ideas?  Starter? Switch of some sort?  If I'm not explaining well enough I can ask
him to post to explain better.