How to use jquery to find the element with display=none and return the elements id to a variable?

I don't think that you need to add :hidden psuedo selector. The following will give you the id of selector irrespective of whether it is hidden or not.

var elementId = $(".galleryitem").attr("id");

but if you add it will be bit faster-

var elementId = $(".galleryitem:hidden").attr("id");