The Printer is a HP Photosmart Premium Fax C309 series. The noise is getting worse! It's in the top lid, paper feed. I believe this paper feed is only used for scanning documents. I've never used it before. But it always activates when you first turn the printer on. The other day I decided to try it out. I figured since it is making noises, that perhaps it wouldn't work. Odd thing is, it did work. Just made noises. I agree with you, it does sound like something got into it. It sounds like that whatever it is, is rubbing against the gears. I'd guess that if it was a bug, the bug would be destroyed by now. Anyways, there is a lid that you can open. But you can't see anything.
The Top of the Printer (Where the noise is coming from)
Opening the Lid (Can't see anything)
From the Bottom side. (Scanner Lid up)