I already posted this in the Accord section, but it is more relevant here I think:

Hey all, new here, this is my Honda I have owned for about 3 months now, I am coming from the truck world
Work on cars all the time, but this one has me stumped.
Car is a 1994 Accord coupe
F20B swapped, with OBD1 and a H22 5 speed trans
It has a new battery, new starter, and new battery terminals

Issues:
Randomly it woulden't start one day, just a "click" and then nothing. Got a jump and it started fine, drove to walmart and exchanged the battery (only 2 months old) but they did not check to see if it was bad or good, just swapped it.
Okay, so new battery ---> the car was fine, started and drove and shut it off probably 5 other times during the day including a 1 hour trip without incident. Went to the store late at night and come out to another no start. A guy jumped me in the lot and it was fine.
Drove to a car meet 2hrs away the next day and it started throughout the day a couple times. Parked it at home and the next morning, a no start. So I had my friend jump me while parked, it fires up fine. Drove it around to see if the issue persisted, and whenever I shut it off it has to be jumped.

So currently:
Today the guy at autozone checked the battery with the fancy checker or whatever, and everything showed fine except the starter. So I grab a new one and installed it tonight, still nothing even though the battery shows fully charged on my battery charger box.

In summary:
It can be jumped started always
It can be started by popping the clutch always (had to do that to leave autozone)
Usually will not start after shutting it off
When attempting to start, it will "click" once, loudish, and then everything will shut off (all accessories) and when you take the key out and turn it to accessory mode nothing happens (it is as if there is no battery at all or something) - wait 30 seconds to a few minutes and it will let me try to start it again, then "click" and repeat.

Seems to run great when jumped etc, idles fine
I am stumped and really need this baby to drive to work
Starter relay? Where is that located and will a local auto store have one?

 

If you are turning the key to accessory mode and nothing is happening I would suspect the ignition switch is bad, assuming the battery terminals are new and the battery is new. It's a really easy part to swap it out and it's fairly cheap at around $30 or so. You can test it by turning the key to acc and testing to see if there is voltage coming out of the acc solder joint at the ignition switch.

How to replace the ignition switch or troubleshoot (Honda, Acura)

Use that site for specific testing.