Well, one thing is obvious- I am manifestly uneducated about this whole subject! But interested nonetheless.
Unfortunately for this subject you'll actually become MORE uneducated on it by reading WingNutDaily articles and basically all the posts about it on FR.
1) The accepted theory of Petroleum formation is that it's made out of ancient dead ocean and lake microscopic plankton (diatoms, algae primarily); there are no dead dinosaurs in oil.
2) There's immense amounts of evidence that 1) is true, including petroleum fields being chemically identical to diatoms in composition, etc.
3) The OVERWHELMING majority of petroleum geologists believe 1); there's been no sudden rush to belief in abiogenic oil by huge numbers of people IN THE FIELD despite claims to the contrary. THERE HAS been a huge increase in the fascination with abiogenic oil by clueless uneducated dilettantes, largely for political reasons.
4) Any organic materials of any kind can easily be buried to virtually any depth through tectonic processes and lots of time. If you reject plate tectonics, or believe the earth is 6,000 years old, you're basically beyond hope and you're impervious to reason.
5) Claims that all over the world many oil fields are mysteriously re-filling are flat-out false.
6) Natural Gas and Oil are quite different; Oil is far more complex.