black streaks across them, as if something has leaked
Across the page or down? Does it smudge?
If it is across, there's a line of spilt toner on the paper path, probably on one of the rollers. If it doesn't smudge, it's before the fuser, if it does it's after.
If down the page, there's a patch of toner that the paper is dragged over.
All you can do is try to clean the inside of the printer with a soft brush and a vacuum - you should use a vacuum cleaner with a microfine filter, because toner is a very tiny particle size.
SD