I'm a little surprised nobody has mentioned "Los Chinos" yet. These are small-ish (actually, not so small in many cases) stores which are owned/operated by Asian/Chinese families throughout Madrid which sells mainly Chinese-made products but cheap. The quality is questionable but for some basic things (like decks of cards, lighters, plastic flowers, etcetera) they can be a cheap shopping option. I don't know if they sell blow dryers but some probably do as they often sell small electronics like radios, CD players, music boxes, etcetera.

Saludos, MadridMan