91 Honda won't start

Bear with me as I do not know all of the correct lingo...
my accord is pissing me off...it won't start. My boyfriend who is mechanically inclined, went through my car and does not no where to go next. We replaced the battery, ground, plugs and wires, but still it won't start. It is turning over and he has spark to the plug but it own't fire. Others have thought that maybe it is the timing gears (?) because when it would start... sometimes randomly it wouldn't start... I could wait a minute and then it would start. Both hot and cold it would do that to me. While driving it would sometimes sort of cut out and act like it wanted to die, but if you put your foot in it, it would take a minute, but then pick up. When it idles sometimes it acts like it wants to die, and sometimes if it were in park the rpms would go up and down between 1000-3500 by itself while idling. There are a lot of miles on the car about 270K, but I have to have it to get to school. The gas milage while I was driving it was awesome, and when it was running it ran great except for the problems describd above, but now it wont start at all.
Any Ideas?

sounds like the dizzy to me.other wise main engine relay.