Hey Toefungus,
I see you are having an issue of a black line in your copies. Are you copying from the flatbed glass or through the Automatic Document Feeder (ADF)?
What model HP printer are you using?
How do you have the printer plugged in for power? I would advise plugging the unit into a direct wall outlet. Sometimes plugging a printer into a surge protector or power strip can lead to lines of this nature due to static build up in the printer. These devices can reduce grounding and cause static build up.
Have you tried cleaning the flatbed glass with a gentle glass cleaner and lint free cloth? As well, try cleaning the small strip of glass used by the ADF when copying/scanning.
http://h30434.www3.hp.com/t5/Other-Printing-Questions/Want-Good-Answers-Ask-Good-Questions/td-p/2094
Jason