It's a completely impossible fantasy. DNA has a half life of ~500 years. Mammoths only died out around 10,000 years ago, which is why it's conceivable that one could be brought back, but all dinosaur DNA has been destroyed for millions of years.
DNA is not a radioactive material. It decays, but there's no absolute law like the radioactive decay, where the half life is the same for every microgram of the same substance everywhere in the world. The average half-life may be 500 years, but there can be situations where the DNA is exceptionally well preserved due to local circumstances. As a simple analogy: the average half life of a human settlement is, let's say 50 years. That means we should see absolutely no traces of human settlements older than 2000 years (40 half-lives). That is far from true.
No molecule is 100% stable... Every molecular bond will break eventually due to random thermal noise...
but:
Researchers in 2016 measured chloroplast DNA in marine sediment cores, and found diatom DNA dating back to 1.4 million years.[62] This DNA had a half-life significantly longer than previous research, of up to 15,000 years. Kirkpatrick's team also found that DNA only decayed along a half-life rate until about 100 thousand years, at which point it followed a slower, power-law decay rate.
Okay, so you're 1/45th of the way there.
And that's not even getting into the complex interaction between a mother and her unborn child, including cytoplasm, mitochondrial RNA, etc. It's not like an organism springs whole cloth from DNA alone.
We have animals now that are closely enough related to extinct animals that we could conceivably bring them back through incremental genetic modifications.
For example, if we wanted to bring back Direwolves, we could edit the DNA of a gray wolf maximally such that it can still be fertile and be born by a non-edited gray wolf. This would give you a wolf closer to a Direwolf and then you could repeat this process using each previous generation as the carrying mother for the genetically modified embryo.
I don't think that's true. We raise animals without their parents all the time, both on farms and in zoos. The animals we end up with are still recognizably horses or rats or chimpanzees, with unique behavioural traits that could be studied for years. Even if you lose the social structure of mammoth society, you would still be bringing back something fascinating.
Animals that can be hatched from eggs have even less dependency on their mothers, too.
I have 16 chicks in the brooder that have never been around a chicken. They never will be around any but their 15 "siblings."
They're still acting like chickens, and they will continue throughout their lifetimes.
If you were to clone a New Yorker thousands of years from now and put them in an exhibit in a Zoo marked "New Yorker", lots of people would be very impressed, even if they didn't start cooking New York-style pizza.
It's unlikely, we'll see.
And they tried really hard to get something out of the really good Mammoth DNA from Siberia. The blood was still liquid. No chance so far.
With today's technology could we create a creature from long ago with nothing more than it's DNA?
It’s harder the older the sample and vastly more difficult if few closely related species survive.
Dinosaurs have enough cultural prestige that it would make total sense to do it as a vanity project if the technology is there.
Similar to turning lead into gold -- there's enough cultural meaning built up around it that someone should do it before it really makes sense in a vacuum.
Even if we got really really lucky and found some that had spent most of its existence frozen deep in Antarctica or something, that would only open the potential of restoring a single dinosaur lineage and not the vast array of species depicted in Jurassic Park. That's total fantasy.
Using numbers taken from http://news.mit.edu/1994/safe-0105 for napkin-math:
Average background dose/year: 500 millirem
LD50 instantaneous exposure: 450000 millirem
LD100 instantaneous exposure: 600000 millirem
Radiation exposure of our dinoDNA sample: 65 million * 500 = 32.5 billion millirem.
Obviously there's a lot more to it than simple dose adding, but this gives you an idea of just what deep-time DNA recovery is up against.
Like hyperbovine mentioned, there are actually other effects that come in to play far sooner, but radiation puts (an additional) hard cap on things, and is easy to napkin-math.
Could you describe half life here? So suppose the strands are now small snippets. If you find enough, couldnt you overlap common parts and eventually re-construct the full length?
Being in amber might protect from moisture, but I think the temperature and temperature swings would still likely destroy it within thousands of years.
.. Except for the DNA that has survived and been passed down to living species today.