It's a cardboard box that used to store my desktop computer. So the outside of the box is not plain and has printed pictures and words. I wonder if it's OK to use the box as a piece of checked luggage.
Yes, it's fine, I've shipped this baby as checked luggage multiple times:
They'll just stick the baggage label on the side.
My main concern was damage from baggage handling, getting wet, etc. Tape it shut carefully, and a plastic bag on the inside would not hurt. Ask for a fragile sticker at check-in, and they'll probably make you sign a disclaimer saying it's not the airline's problem if it breaks.