What if the DNA was frozen?
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.