Same thing happened to my 97 accord a few weeks ago. I replaced the starter and the battery under warranty. Everything pointed to the starter being bad. Turns out just by luck I started looking around the engine compartment and at a glance I happened to see that the negative battery cable had broken in 2 where it connects to the transmission. This stopped the starter from working but allowed everything else in the car to still function. If this is your problem it will be very cheap to fix. Go to a parts store get a 2 foot battery cable and replace it. Although the one I got at pep boys had a smaller Guage wire for the chassis ground. So I'll be getting one from honda for piece of mind.