You don't need an alternator to fire up. Commonly we use cranks and turn over to mean the same thing. Gathering that you are using turns over to mean that the motor starts and runs, aka fires up.

Do you hear the fuel pump priming when you turn the key to on w/o starting it?
Do you have injector power?
Do you have injector pulse?
Do you have spark?

Really it comes down to three things. Fuel, spark and compression. We assume compression hasn't changed in all 6 cylinders.