As a geologist in spe, I've heard a lot about the Cretacious - Tertiary boundary. (fun fact: "Tertiairy" is outdated, but everyone uses it anyways. XD "Cenozoic", that's what it is...)
There are many clues that could lead to the commonly accepted projectile from space-theory.
Not only was the Yukatan crater dated at around 65Ma, everywhere in the world as thin layer containing the element Irridium can be found. This layer had also been dated at around 65Ma. The worldwide appearance of this layer tells us that around the C/T boundary the climate suddenly gut diverted from it's usual pattern.
Many believe that the impact of the Yukatan projectile, caused dust clouds into the sky. Combined with a heightened Vulcanic activity, this caused the worldwide climate to change.
Image that in 1991 there as a huge the volcano Pinatubo's (Phillipines) (in combination with others like Mount Hudson's (Chile) in that same year) caused a change in the seasonal pattern. Multiply this effect with the amount of activity around the C/T boundary, and you get a climate that's hostile enough to kill a race as develloped as the Dinosaurs.
One theory is that the mammals, being small and still in full devellopment, got the chance to addapt quickly to this new condition, and thus they survived.
Another theory, regarding the Dinosaurs' long life of about 200Ma (251.0 ±0.4 Ma/Start Triassic - 65.5 ±0.3Ma/End Cretacous) were just tired of living. The species had the chance to roam our earth for so long... that they eventually grew bored and left. Or so to speak.
Truth is that something changed on our planet 65 Ma ago. The dinosaurs weren't the only one to go.... And the C/T extincion is just one of the many that our planet's history went through, and will go through.
I learned something last year:
"Once dead, always dead."
So no rebirth.
Except... when you go count in the "Lazarus-effect" like the Coelacanth... which wasn't so extinct as scientists believed it was.
Edit: Carbon dating is mostly used for the more recent history, i.e. Human history. Earth's history is measured by other isotopes such as O δ16,18, S, K/Sr... etc.