The starter drive (aka bendix) is broken. The bendix and/or starter needs to be replaced.
The woo woo noise you describe sounds like the starter is trying to spin. The bushings inside the starter are probably worn, causing the starter to drag. When the starter drags, it cannot spin fast enough to start the engine and the worse it drags, the less it is able to spin.
You need to replace the starter.
Heavy corrosion will prevent enough power from getting to the starter to spin fast enough to start the engine.
Usually when a starter solenoid/relay switch is bad, you will hear only a click and the starter will not spin (crank).
When and if the engine stops at the point where the starter gear is aligned with the missing teeth the starter will just spin and not start the engine. Over time even if the starter turns the engine over it will eventually ruin the starter. You need to replace the flywheel and the starter immediately.
the armeture is shoeted. replace the starter.
There is many different things that can be wrong. If you have lights but the starter won't spin, then you could have a bad break light switch,a bad starter switch, bad starter solenoid, or even a bad starter. If the starter does spin but the motor won't start it could be a bad spark plug, bad coil, fuel blockage, carburetor that needs to be cleaned out, or bad stator.
You may not have hurt anything. The starter will spin as long as the cable is sending power to it. The ignition switch needs to be turned on to make this work. Touch the jumper cable to the starter connection. The starter will spin and start the engine, assuming that there are no engine problems. This is a dangerous move, because if the car moves or it is in drive, then the car will drive over you.
because its gone bad the starter solenoid is engaging the gears, yet the motor fails to spin
the starter
that sound is most likely your starter engaging. a starter has two components an electric motor and a solenoid that pushes the gear into contact with your fly wheel as the electric motor spins the gear. sometimes just one one component will fail and still allow the other to operate, Hench the clacking of the gears engaging but no spin.
Have you checked the air filter? Fresh Gas? Battery amps?Does the starter spin and not engage? If so it is your starter solenoid.