OK I have a 1991 Civic wagon.
It has the following done to it B20 swap.
The issue I'm having is when it is cold outside the car will not start.
From what I understand the P.O. had been trying to figure it out for abut 4 years.
So turn the key to start (when cold outside), all the lights are on (dash) you can hear the pump turn on but the starter will not fire.
Basically you will not get the starter to engage (if you hold the switch 3 seconds it will pull in the starter (but you better make sure it runs at that point or it will not crank again)
If the car is warm it engages and starts.

I've changed the following:
main relay (starting got a little better but not fixed)
starter relay (no change)
ignition switch (starting got a little better but not fixed)
main fuse box in engine bay (no change)
starter (P.O. changed (then we put jump switch on and it will start all day long))

Any body seen issue and how did you fix it.

I know the wagon does it and my buddies hatch is doing it.

 

Sounds like the voltage is too low to engage the solenoid. I would put a volt meter on the starter solenoid and see what you are getting while trying to crank. Then check voltage at the battery during start attempt. If you have a voltage drop across those 2 points you will need to chase that down (bad cable, loose or dirty connectors, etc). Things shrink in the cold, so a loose connection is a good bet. The more amps the cleaner and tighter connectors need to be.

Edit: if you have low voltage at both points and you know your battery is good, check your ground cable (replace or clean ground connection point).

 

Sounds like bad ground or poor battery.