My 86 crx and my dads 88 prelude had the ignition wiring that went bad. These two cars are long gone now. I even figured out the problem myself on both cars. It was like you were turning the car off at the same time you were trying to crank it. What was bad on our two Hondas was the wiring behind the key thing that turns. Don't know the exact name of it. It's not to hard to change. You may want to check that if you can't figure anything else. I can't remember exactly how i figured out this was my problem. Maybe the radio or something came on and turned off when it should have been on. That led me to believe it was the ignition wiring switch thing. Also, it quit, barely started back, and then eventually would not crank at all. And yes, they turned over, but just would not crank.