hard starting

first thing in the morning car doesnt want to start. can crank it over and over but wont fire off. After it finally starts there doesnt seem to be a problem as far as shutting off and restarting. Just the initial start up.

Intermittently the car wiil not start after being driven. Can drive twenty miles, go into a store for maybe 15 minutes, come out and it cranks really slow like a low voltage on the battery, but the more it cranks the more speed the cranking picks up. It is like it is vapor locking but not sure about these newer cars.
2003 mazda protege 5 wagon 2.0 a/t
Any help or ideas

hmm i think this is in the wrong section.

Does the car always eventually start? And when it does start does it just slowly sputter to life or doesn't it just randomly start up like nothing is wrong?

this sounds like you have some fuel delivery problems

the extended cranking sounds like possibly a fuel pressure regulator

the hard starting on hot restart could be related to the extended cranking problem

as for the slow cranking on hot restart im still trying to figure out

weak or bad coils can also cause hard starts

but with weak coils you would also most likely have stumbling under high load
and the op doesnt have any other drivability concerns

just starting problems

when it decides to finally start, whether first thing in the morning or on a hot start, it takes off like nothing is wrong. I thought about the regulator as far as the extended cranking but the slow cranking thrown into the mix aids the head scratching. I thought I might check here before i start throwing money at things on a whim.
As far as first start here is my method for better understanding:
Make sure all accessories are off, turn key to on position and listen for fuel pump to come on, turn the engine over an appropriate amount to start the car under normal circumstances. Maybe seven revolutions at most. turn off key, turn it back to on position and listen for fuel pump delivery. Basically thinking that if nothing else I am priming the fuel system. Continue this method until start up. normally after four reps it will fire up.
Just so you don't think i am cranking this thing until the battery is dead and crying about slow cranking. The slow cranking is always there. The battery cold reads 12.6 volts, and says it has 675 cranking amps, and 525 cold cranking amps. battery is probably a year old and i haven't experienced this problem until now.

slow cranking almost sounds like a loose conection or high resistance in the starting circuit

check all of your connections at the battery, starter, etc