The sound you are hearing is the starter motor turning without engaging the flywheel.
Tech content to follow.
1) You turn the key to start.
2) Ignition switch connects a 12 volt low current connection to the starter solenoid.
3) The starter solenoid is energized. The solenoid does two things.
3.1) It pushes the bendix bevel gear into the flywheel. the bendix bevel gear is heal away from the flywheel with a strong spring. The flywheel has gear teeth on it's outer rim. The bendix bevel gear engages the teeth in the flywheel. The starter motor will turn the bendix bevel gear and hence the flywheel to start the car.
3.2) It closes a high current relay to energize the starter motor.
When your battery is weak, there is not enough current flow through the solenoid to push the bendix bevel gear far enough to engage the teeth on the flywheel. There is enough current to cause the starter motor to turn, but since the bendix did not engage the flywheel, the car does not start.
The sound you hear is the starter motor turning without engaging the flywheel.
good luck,
Ken - West Union, SC Population 270 + 2 (counting dogs and chickens) "If you only have a hammer, you tend to see every problem as a nail."
I'd start with a known good battery, but my experience is that if the starter turns but won't engage flywheel, more than likely you need a new starter. If you can get to it with a long screwdriver, a few raps with a hammer will often allow the bendix to free itself and the car will start.
In either event (battery or starter), these are relatively inexpensive repairs and are easily done by any decent garage or handy DIY'er.
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