I had the same problem with my HP photosmart 7450. It started with frequent paper jams, to the point where it happened everytime it pulled the paper in to print. I had the rattle also, turned it upside down and the pin fell out, just like yours. I'll bet it's happening to many other 7450's. Anyway, I was able to repair it myself.
The pin attaches to a small black plastic gear, about 1/2 in. in diameter, in the paper feed roller, (on the right side, and not visable from the front). I had to remove the misc. covers, several screws attaching different things, includind the sliding ink absorber on the right side, (that was fun) to where I could see the loose gear. This was no easy task. I'm an auto mechanic, so I enjoy a challenge. However, as much as I like the printer, I was ready to toss it in the dumpster if I couldn't figure it out. First you'll need a small "torx" screwdriver or two, as well as some other basic tools. If you're patient, good with your hands and have a good sense of how things work, you can probably repair it yourself also. Let me know if you're successful.
Good luck!.....Ron J........
[email protected]