Hello Guys,

I have a '99 Accord V6 EX Sedan.
This last year, my car started violently shaking on startup and it would sometimes turn off right after starting up.
The mechanic replaced the EGR and Starter, but that did not solve the issue.
I replaced the main fuel relay, fuel pump, and 4 out of 5 motor mounts (they were bad) and that fixed the issue for a while.

These past couple months, the same (or a similar) issue came up;
I would start it up and the engine doesn't rev up too much, it would rumble and slightly shake the car, then turn off (the lights would stay on).
It only occasionally happens, and it tends to happen more when the engine is hot.
When idling in park, it idles at 750rpm but after a while it drops 100-150rpm then comes back up (I do not know if this is normal or related).
Once my car is started up though, it drives like a dream. No issues accelerating or stopping at a stop light.

I thought it could be a fuel/air problem, so
I replaced the air intake with a cold air/ short ram intake because the resonator box had been broken in 2017 from a minor crash (this never caused an issue though).
I replaced the throttle body, IAC sensor, alternator, accessory belt, battery.

I do regular maintenance on it; replace the spark plugs once a year, and oil every 3-4k miles.

One thing that worries me is that there was a small puddle of coolant behind the air intake, near the engine.
This might have happened when I took off the old air intake; I'm hoping it's not leaking directly from the engine.

I am going to replace the ignition switch and see if I can find a coolant leak, but besides that, I am all out of ideas.

Any suggestions would help. I can do most of the work myself. I'm hoping not to have to go to a mechanic.