Could be the starter sloenoid, loose connection (wires to the starter), faulty relay or the ignition switch????

I had that happen with my Teg, I took out the starter and had it checked at Autozone, put it back in and it worked fine. Probably just a loose connection that I fixed by putting it back (or it just needed to be reassured that it was still good).

I too have 320,000 miles on my 92 4dr Civic. Just about the only original parts left are the motor, starter and most of the interior electronics. Love these cars.