There are plants that will tolerate those conditions but I am not aware of any that would withstand your climate. I'd be inclined to just use containers of colorful annuals to brighten up the area.

The boxes are under some kind of broad-leaved tree, with pine trees looking on from behind - which area are you asking about?

Otherwise, yes, if you are having trouble using the boxes where they are now under the trees removing them and trying new plantings elsewhere on the site - probably directly in the ground, without any planters being involved - could turn out to be a lot more rewarding.

nothing grows there

A lot depends on what, specifically you want to grow and what your gardening habits are. I, for instance seldom try to grow vegetable plants because I don't get back to them often enough to get good results.