I presume you don't mean it's skipping lines of text as such, but rather that text/pictures/whatever have horizontal white lines through them, probably regularly spaced.
I don't think alignment will help, but if it improved somewhat after the first head cleaning cycle it sounds very much like a clogged printhead. Was the printer left unused for a while, maybe several weeks? They do like to feel wanted, and keeping them somewhere warm is a bad idea as that too can cause the printhead to dry out.
Unfortunately, if its out of warranty, once this has happened there's not much you can do apart from repeated head cleaning cycles until you run out of ink. Check whether there's any kind of deep cleaning cycle amongst the maintenance options.
There are a few kill-or-cure measures you may come across with a bit of googling, such as manually moving the print head away from its rest position then inserting a paper towel under it and soaking it in cleaning solution, but these are desperate measures