Why does car make whirring noise but not start?

From most to least likely:

1. Starter solenoid is not getting power

2. Starter solenoid is bad

3. Starter gear is stripped

4. Flywheel ring gear is stripped

Age of starter is not really relevant. It is possible to get a defective one.

Check electrical connections. Some cars have a separate wire to the solenoid.

Remove starter, look for obvious damage to gears.

If you don't see anything really glaring, like a chunk of flywheel missing, take the starter to any auto parts chain store. Most of them have a testing setup and do the testing for free.