Dimitri, your motor should still be fine. I accidentally started mine with the indexing button (spindle lock) engaged several times and it survived OK. The slipping belt makes a horrible screeching sound, but my motor never showed any signs of problems. As you learned, though, at the first sign of trouble, hit the power switch first. Trying to disengage the spindle lock with the motor turned on could be dangerous.
The ticking you're hearing could be several things. One thing to check is that the set screws that hold the stationary halves of the pulleys onto the shafts are still tight. You should also inspect the main belt carefully to see it there are any torn or frayed parts. I don't know if you've seen it yet, but there's another, smaller belt deep inside the headstock that connects the motor to the Reeves drive. It may take some work to get to them, but you can also check the set screws on those pulleys to see if anything is loose.
Another thing to try (very carefully, I should add) is running it with the headstock cover removed. If it
is something hitting the inside of the case, the noise should go away with the cover off. And if the ticking sound is still there, you know it's somewhere deeper inside the headstock, but with things visible it might be easier to track down where the noise is coming from. Also, while you have it open, try adjusting the speed up and down a few times. Being able to see it in action will help you better understand how the Reeves drive works. Just be sure to keep fingers, clothing, and hair clear of any moving parts.
You mentioned the spring on the top pulley, and that reminded me of another safety thing to keep in mind when you're working on your lathe: That spring is VERY strong, but still, sometimes the upper pulley gets stuck in the "wide open" position. If this happens, you can often unstick it by tapping the pulley lightly with a plastic or wooden mallet. But when you do, be sure your fingers are not in between the two pulley halves, because when it gets unstuck, it will snap shut like a bear trap, and will definitely damage any body parts that happen to be in the middle. I came very close to getting a finger caught in mine the first time it got stuck. After that experience, I was very careful when dealing with anything around that spring. At some point, you'll likely need to remove the spring and disassemble the upper pulley. (To change belts, for example.) The website I linked to above has good instructions for disassembling it. The main thing is to make sure the spring is restrained when you remove the clip that holds it in place. Darrell shows the device he made to release the spring tension safely. I made one similar to it, and I would want to try taking the pulley apart without it.
Good luck in your search for the problem, and keep us posted on what you find.