Challenged wrote:

> 95 Integra LS (92K mi) - New battery, New ignition switch (Key
> cylinder), Verified working main relay and fuel pump.
>
> A few times a week, there is dead silence when I turn the key. I would
> do this a few times and sometimes on the 3rd - 10th try, the car would
> start, sometimes not. Any ideas on where to start?

Sounds like a zorched starter solenoid.

I don't know anything about a 95 Integra. Sometimes the solenoid can be
changed seperately from the starter, others are integral, and the whole
kaboodle must be exchanged. In a pinch, you may be able to disassemble
the solenoid and (partially) repair the contacts by scraping them to
bare metal.