The answer is no. It is very rare to find any kind of usable DNA in fossils and the oldest limit for it seems to be about 50,000 years ago. So no, there is no DNA to all those fossils the evolutionists cackle about and no, you do not have the education you claim to have or you would know that.
You just proved the YEC's to be wrong. If DNA is totally degraded in remineralized bones after about 50,000 years or so, then we shouldn't have any trouble recovering sufficient amounts of testable DNA from fossils of all types if the earth was only about 6000 years old.
BTW, not all fossils are completely remineralized. DNA fragments can be recovered from some partially remineralized fossils (most notably in the teeth), and in organisms preserved in amber. The following links may provide you with some interesting reading:
As far as attacking my education, forget it. I have the sheepskin to prove it.