Can't help you with the stain question, but...
I had this problem with a Canon printer. Turns out that there is a lot of leakage and overspray in inkjet printers. I presume that HP is the same as Canon in having a felt pad in the base of the printer housing to absorb the overspill. Thing is, especially in an old printer, the felt pad can become over saturated and the ink just dribbles onto your desk.
I bought a new felt pad and replaced the old one. I couldn't believe how much the pad weighed! There was probably hundreds of £££ ($$$) of ink in that pad.
It was a horribly dirty job, but I extended the life of the printer. I wouldn't do it again...
I tried to clean it but, with arthritis in my fingers, I couldn't reach inside th affected part of the casing. I took it to my local cartridge shop and he completely cleaned it, replacing the old pads, etc. for only £15.00, much cheaper than buying a new printer with, no doubt, a significantly shorter life.
What he did recommend, though, was that when leaving the printer for an "extended period" (undefined, but I don't print much any more) the cartridge carrier should be moved to the centre of the printer away from the parking place.
His reasoning is that the heads rest on the absorbent pads and that can start a capillary action which sucks the ink out of the cartridges.
Whether that is a good idea or a bad one I have yet to determine.
