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Hyundai Accent 2006-engine makes a humming sound and the car won't start

I am writing about my Hyundai Accent that made a long buzzing noise with occasional clicking sounds.
Two days ago we pulled over in front of a store to quickly drop my friend off. When I attempted to start the car again to park it a few blocks further, the car would not start (no cranking sound just nothing), and the engine started to make a humming, buzzing noise. The noise would not stop and we called a towing truck. The car continued to make the noise for 45 minutes until the towing truck driver arrived and disconnected the battery. We also would smell a burn with increasing intensity, and about 20 minutes or so in the car making the noise, there would also be some clicking noises.
The repair shop says the car runs just fine now, that it is not making any noise, and they have no idea what the problem may be. They have to wait until it does it again, which is very frustrating. About a month ago, the timing belt broke and the same repair shop had to rebuild the engine. And occasionally we would hear a humming noise when driving the car. I suspect that during the repair the repairshop made a mistake.
Do you have any idea what the issue may be?

If the starter motor gets stuck in the “on” position for some reason it could make a buzzing/clicking noise and the burning contacts could produce an odor. I’d be inclined to remove the starter motor and have it inspected & bench tested w/those symptoms if it happened on my car.