At the very most, you might hope to be able to obtain a dinosaur DNA fragment.  Biologists could only guess at what was missing from the complete genome, without knowing for certain.  It would be like trying to predict the contents, and order, of a complete library of information from the facts contained in just one page of a single book. 

Scientists are currently working on gene therapy for humans, where they target, extract and replace a faulty gene which causes disease.  This isn’t easy, even though the genome for a human is known.  Image how difficult it would be to replace ‘missing’ genes for an extinct animal?
Dr David Stearn has suggested that in the future scientists will be able to ‘map backwards’ to create a complete dinosaur DNA sequence.  Put simply, the premise is that DNA sequences will become mapped for living relatives of dinosaurs (reptiles and birds) and scientists will be able to work backwards from these known sequences to create a dinosaur genome.

However, it must be remembered that a small change in genome can manifest as a very large change in organism (remember the human and the banana!).  Jeremy Austin of the Natural History Museum suggests imagining the dinosaur genome as a jigsaw puzzle with billions of pieces.  Instead of flat pieces of cardboard, each piece is a cube with a different fragment of the overall picture on each side.  To complete the puzzle, not only must each piece be in the correct place, the correct face has to be showing too.  

 
So far scientists have successfully mapped the genome for two bacteria, a

yeast, a nematode worm and, amazingly, for humans.  Let us imagine that

dinosaur DNA is similar in complexity to humans – some 3 billion base pairs.  The human genome project took 15 years to complete with research teams from around the world

collaborating.  It is estimated to have cost $3 billion.   The cost and timescale

to accurately map living dinosaur relatives, and then map backwards from

there, would be immense.