Does time stop at the speed of Light?

I asked a question about Light traveling at the speed of light several years ago, but it cannot be correct.

"Now, we all know that Einstein said that Time slows down progressively for a traveler who is accelerating towards the speed of light. He also says that--theoretically-- time stops for a traveler who is traveling AT the speed of light, and--also theoretically--time travels in reverse for a traveler who is traveling faster than the speed of light. Unfortunately for Sci-Fi fans, he also said that no traveler can ever "cross the lightspeed barrier." Now, get this!

I always knew that Light travels at the speed of Light, and that time does not move for an object that is moving at the speed of light, but I also knew that it was impossible for any object to travel at exactly the speed of light (unless it was a photon, of course). But the light that we see--the REAL light that exists around us everywhere--actually does travel at the speed of light and therefore is always everywhere all at once because it does not take time to get there! If you have ever watched a Marching Band from Upper mezzanine across a stadium, you have seen the "time" it takes for sound to travel at the speed of sound. But how can one imagine that Light itself does not travel in that same sense--it essentially is already there, shining on whatever is in its path for infinity!

But it would hinge on the notion that time stops for objects (or light) traveling AT the speed of light. Does it?