Car problem: Honda Civic occasionally fails to start

I am having an apparent problem with my car. I was hoping that someone would be able to identify the nature of the problem based on the following facts:

  1. My 1994 Honda Civic EX failed to start the other day. Instead, it made a rapid clicking sound when I turned the key.
  2. After several minutes of turning the key, it finally started.
  3. On several occasions after that, it started fine.
  4. The next day, it didn’t start. Instead, it made the rapid clicking sound.
  5. After pressing the brake hard (probably irrelevant), and turning the key, it started.
  6. The headlights, radio, and interior lights seem to work fine (that is, the battery seems to be charged, as far as I can tell).
  7. When I opened the hood, I found that the cable connecting to the red terminal on the battery was hooked up, but could be easily removed (that is, it was touching the terminal, but it was not tightly connected, and could be removed without any tools)

What is the likely problem?

The first place I would look is that battery terminal, it could be connected enough to power the accessories but not enough to provide enough amps to the starter. This could also explain the sporadic nature of the problem.

If the issue continues after fixing the battery terminal then it could be the starter going out.

The brake could be irrelevant or, by hitting the brake and making the brake lights come on the battery could have arced enough to turn the starter over.

Clean and secure the loose terminal. Then see if the problem persists.

This is absolutely a problem. Fix it. Odds are, that’s all it needs.