I have an 07 Corolla with 28k miles and manual tran. After I start the car and back our of the garage, or a parking spot, the next time I apply the brakes I hear a single snap or click coming from the engine compartment on the driver’s side. It occurs only once, and does not occur unless I first back up, then go forward, and only after the car has been shut off. Any insight on what’s happening would be appreciated.
Based on the description, I believe that this has something to do with the ABS self-test that is activated under exactly the same circumstances as when you are hearing this strange noise. That being said, the self-test does not normally make that type of noise (at least none with which I am familiar), indicating that something is probably not functioning as it is supposed to.
A 2007 Corolla with only 28k on the odometer is probably still covered by the manufacturer’s Bumper-to-Bumper warranty (3 years/36k, if I recall correctly?), so no diagnosis is necessary on your part. Take the car to the dealer, describe the symptoms for them, and try to demonstrate the problem for them.
The dealership’s responsibility is to diagnose and fix the problem (which could be serious, since it has to do with the braking system), and your responsibility is simply to maintain the car properly, read the warranty details, and take the car to the dealership for free diagnosis and repair.