Since you have been to the US before I am surprised you don't know what happens.
Even if you missed all the signs and announcements at DEN:
http://www.flyertalk.com/forum/briti...rough-jfk.html
You posted on here and you will note
dj_jay_smith 3 posts above your one said:
For all US bound flights you must clear passport control and immigration at your point of entry into the country. (JFK in your case).
This means that you will have to collect you bags, take them through immigration and then drop them off at the baggage drop counter for connecting flights.
They will be tagged through to your final destination, but you still need to collect them and go through this process.