If there is one day in Semana Santa when just about everything is closed (including El Corte Inglés) it's Good Friday. At least that's the way it used to be. These things can change from year to year. Most stores are closed on Holy Thursday too in most parts of the country, Madrid included. I don't know whether the Corte Inglés is closed on Holy Thursday or not, but as Meg said, you'll probably find the record and book section open. For some reason I get the feeling Corte Inglés is open that day.

By the way, Holy Thursday isn't really a national holiday because in some Comunidades Autónomas (Cataluña, La Comunitat Valenciana, Las Islas Baleares, for example) it's officially a regular work day. Instead they take Easter Monday off.