The theoretical limit for C-14 dating is 100,000 years using AMS, but for practical purposes it is 45,000 to 55,000 years.If dinosaur bones are 65 million years old, there should not be one atom of C-14 left in them.I've been poking about on the internet again (as you do) and found a whole load of stuff by creationists about the problems with carbon 14 radiometric dating.Specifically they report (with some glee) that coal has been found to contain measurable amounts of carbon14 which it should not of course because it is about 300 million years old and dates from the carboniferous period.He said that his team and the laboratories they employed took special care to avoid contamination.That included protecting the samples, avoiding cracked areas in the bones, and meticulous pre-cleaning of the samples with chemicals to remove possible contaminants.C14 has a half life of 5730 years and is only good to date objects to 50,000 years or so.
See also these papers by: Curt Sewel, Do-While Jones, Michael J.
Carbon dating is used to determine the age of biological artifacts up to 50,000 years old.
This technique is widely used on recent artifacts, but educators and students alike should note that this technique will not work on older fossils (like those of the dinosaurs alleged to be millions of years old).
The preferred method of dating dinosaur fossils is with the radiometric dating method.
And the result of this accepted method dates dinosaur fossils to around 68 million years old. Its half-life ($t_$) is only 5,730 years—that is, every 5,730 years, half of it decays away.