Hi WaTz, and welcome to our forums!
I'm sure this is not the answer you want, but according to standard theory massive objects cannot move at the speed of light in a vacuum. Therefore the question of time dilation at the speed of light in a vacuum does not have an answer, because current physics don't allow it.
You can read more about that
here. (The front page of the same site is
here). It is not a new article but the text is still quite good.
All the best,
Tormod
