Car turns over but won't start unless car is still semi warmed up from previous start?

I have a 96 Honda civic ex, today I spent 5 minutes trying to start the car, the engine was turning over, it wasn't turning over slowly. The starter is testing fine first off. Car starts fine if it's still warmed up from previous start, pumping the gas doesn't help. Today, for the first time it got to the point where I had to push start(pop the clutch) to start the car, and had to do it a second time today. So it does start by push starting. Where should I start? It's a d series engine. Dy16 or something like that

Clean the battery to body earth connection, and the earth connection
to engine, this will be mating better when warm, but if there's any dirt/slackness, there will have been arcing which helps to take away the full mating surface when cold, this will prevent a good contact,
a regular occurrence on older cars, because of years of vibration, dampness, etc.

The pgmfi (main relay) is bad. You can either remove it and have it re-soldered or just replace it.