This might have to do with the throttle cable, checkout this thread on the honda-tech forums: http://honda-tech.com/honda-civic-del-sol-1992-2000-1/how-do-i-adjust-my-throttle-cable-2868260/ This video shows a solution to a similar problem with a 2002 Accord: https://www.youtube.com/watch?v=AuOBuNaH... Hopefully this helps!
This may be too late but... I had this problem with my 1999 Camry and it turned out to be a bad starter motor. At first tapping on it would allow me to start the car but after a while it'd take more and more until at one point it just stopped starting period. If this turns out to be your problem it's a pretty cheap and simple fix to do yourself for the most part: pick up a starter at O'Reillys , pop the old one out and the new one in. It was pretty straightforward so I didn't use a guide or video but this video seems to be a good start.