The half-life of DNA is about 500 years; the odds of finding any preserved sequences of dinosaur DNA longer than a few base pairs is pretty much nil. Even with very large samples, it simply would not be possible to recover any information from such fragments any more than you could reconstruct a book from a list of the syllables contained in a few million shredded copies.
You'd have an easier time modifying the genomes of modern-day birds and reptiles to produce something that looked like dinosaurs, but even this is far beyond the reach of current technology.
There are some birds even now that are "obviously" theropod dinosaurs (all birds are dinosaurs, but some are phenotypically closer to their ancestors than others). The sauropod lineage is truly dead though – birds are still their closest extant relatives, but the lineages diverged already in the late Triassic, ~230M years ago.
With the benefit of hindsight, it's a bit surprising that the link between ostriches and raptors (first fossil 1923 I think) in particular wasn't more noted which, of course, would have implied some link between theropods and modern birds more generally. There was some evidence like feathers on some dinosaurs but thinking about dinosaurs didn't really start changing en-masse until the late 1980s.
You'd have an easier time modifying the genomes of modern-day birds and reptiles to produce something that looked like dinosaurs, but even this is far beyond the reach of current technology.