Actually, we have DNA which has survived for tens of thousands of years. Unfortunately the dinosaurs died out (except for birds which are descended from dinosaurs) many millions of years ago.
Recently, it's been claimed that some fragments of DNA molecules (not actually DNA) have been found in dinosaur fossils. Could be, but the would retain no information about dinosaur genes. Jurassic park, I think supposed the DNA of dinosaurs could be found in mosquitos trapped in amber. That's been checked. No such luck.
You might get some ideas from bird DNA, but since they evolved from one highly specialized group, and have been evolving for many millions of years, I think it's unlikely.
Michael Crichton can tell a good story, but his scientific knowledge is seriously lacking.