Starter on 1200 L 2006 whirs but does not engage engine to start

your starter is not fine and how was it checked --your starter gear is not engaging ---------A whirring noise occurs when the starter pinion gear freewheels during the engine cranking. This is because the pinion gear is not engaging the flywheel properly, which will also cause the engine to fail to start

Starter pinion gear not engaging. Motor is turning but gear is not transmitting the energy to motor for start purposes.

Make sure battery is fully charged and try to start - if nada replace starter.

The solenoid located on the starter most likely has a wire either not connected,or open or the solenoid itself is bad(Check the wiring with known good pictures of the assembly and then use an inspection mirror to check that the wiring is securely mounted and then go from there(starter draw tests,jumper wire the solenoid itself)Its seems to be that the poles in the relaying mechanism in the solenoid aren't drawing the starter bendix in order for the spinning motor to engage the ring gear itself,thus you only hear the motor whirring but no magic,Jason...

check battery power and its charging otherwise selfstater problem

12.6V is kinda low for a car battery. It should be closer to 13.8V with the engine off. I would try jump starting the car using another car/battery and if that works then have your battery load tested as it may be on its way out. If the battery load tests fine then I would look at the alternator or see if you can swap the re-man'ed starter for another one

I'd have to make sure battery has a full charge and battery connections all good. You can use digital multimeter across battery posts, everything off, the generic spec for a full charge is around 12.6 volts. If the battery is down, get it charged up. We can't do any testing if the battery is down.
On further testing, you can take starter motor off, lay it on the ground. Hook up jumper cables properly from charged battery to starter motor, at the least, the starter motor should spin and kick out the drive gear. If it won't do both, then I suspect the starter motor has a problem. I only mentioned the starter motor because you heard a whirring noise, maybe that noise was the starter motor spinning but not engaging the flywheel, for some reason.

Sounds like the starter sprag clutch on the flywheel is slipping.

maybe, now this is just a guess! but your starter shaft is just spinning and not engaging properly..check starter or solenoid to starter wire connections are that they are on solid, and no corrosion, measure bat volt!!!... should read 12.4v "minimum"! if not battery is either going bad or might need a charge...correct voltage reading should be 12.7v to 13volt.

you'll need to pull the starter. It sound like your Bendick's is bad. that's the upper gear drive assay. the only other res ion would be, low power to the starter, and not receiving an acquit amount of amp to reach the rpm's it needs. good luck

WELL SOUND LIKE STARTER IF YOU CAN TAP STARTER WITH HAMER IT MAY MAKE IT WORK BUT YOU WILL NEED SOME ONE TO TRUNE KEY FOR YOU IF IT DOSE MAKE IT WORK REPLACE STARTER BUT MY MONEY ON STARTER