Why won't my printer pick up paper?
The paper is in place. The printer sounds like it is trying to pick up paper but paper does not feed.
The printer’s paper pickup rollers may be dirty and need to be cleaned.
Here’s a link to a video which shows how to clean the rollers for a HP Officejet 4620 (I realize that this is not your model but it is in the same series -Officejet 4600 series - so it should be the same procedure).
The section of the video dealing with cleaning the rollers starts at 4:10 minutes into the video and finishes at 10:02 minutes into the video.