My printer had the exact problem. I used to have a little brother. Used to.
Every time the printer turns on, does the paper eject out of the printer at a faster speed than the last? If so, the printer is trying to kill you. It is testing its stabbing power. Sooner or later it will eject with enough force to cut a human being in half. I see you mentioned it printed out a blank piece of paper. This is bad news. When, or if it runs out of ink, that will not be a problem. It will continue to eject blank pieces of paper until it can kill you. Best solution is to get rid of the printer.
You have been warned. I just don't want to see a fellow forumer-goer end up like my brother. I wish you luck.