I have a 95 Integra Special Edition as well. I have the same problem. There's nothing wrong with the battery or alternator. I have a feeling it has something to do with the alarm system it has in it. The only problem is that I don't know if my alarm system came with the car or if the previous owner installed it. I'm it's new owner and this problem has happened twice now.
Every once in a while, when I go to start it, all I get is a click from the Starter. It's not trying to turn over or engage or anything. The battery is fine and it did the same thing when I tried to jump it. If AAAnybody has any idea what causes this I'd really like to know because it's veeery incovenient.


EDIT I found this, maybe it's the problem/solution?
http://yotarepair.com/Electrical.html
It's the same problem I'm having but it's on a Toyota.. can't be too different.