First off, it's not going to be the starter or alternator. Not a chance for either of those 2 if it cranks over and over and over.
My vote is the rotor button in the distributor is wore out. Very cheap fix too if it turns out to be the problem. Even if it isn't, it's a cheap part and needs to be changed out every now and then anyways. If you have tried to crank the car enough after changing the spark plugs again, they may be fouled out.
On my roommates honda, his rotor button was wore out and we replaced it, but it seemingly didn't fix the problem. However, he had flooded the car out attempting to crank it so many times, so we replaced the spark plugs and she fired right up.
Pull a spark plug wire and stick a spark plug in it. Turn the motor over and get somebody to see if the spark plug is sparking. If not, then it's definitely a spark issue (obviously). Try changing the rotor button, and re-do the test. If it's sparking, then that fixed the problem. If it still doesn't crank, change the plugs again.