Don't mean this to be nit-picky -- it's just very confusing when wrong terminology is used. When an engine is "cranking," it's "turning over."
They're the same thing. The battery is giving current to the starter motor and the starter motor "turns over" the engine -- it "cranks" it. The engine may or may not "start" and "run" because
that requires spark, fuel, air, and compression. Cranking (or turning over) only requires a good battery, starter, ignition switch, and interlock switches. As I said, I don't mean to sound offensive, but it's difficult to figure out where a problem is if the wrong terminology is used.
Uclaccord -- you said,
"... i only have this problem when i make really short drives, park, then try to start the car again w/in a few minutes .."
This sounds like a temp sensor problem. Honda temp sensors frequently "die cold." Here's what I mean: When you start a cold engine, the temp sensor puts out about 1V, to tell the ECU the car's cold. So the ECU dumps a lot of fuel into the engine to help the cold start. As the engine warms up, the temp sensor voltage will rise... up to about 5V for a fully warmed up engine. So the ECU leans out the fuel supply and drops the idle speed.
But then, for some mysterious reason, the faulty sensors will "die cold" -- they'll go back down to 1V even though the engine is warm. You can drive around like this and never notice the difference, cuz PGM-FI is compensating by using input from other sensors. But when you try to RE-start the warm engine, the temp sensor (at 1V) is telling the ECU the engine's cold. So the ECU dumps too much fuel into the engine -- and floods it! As soon as the sensor and the engine cool off a bit, the car will start again.
Hope this helps.