Finding a boolean submatrix isomorphic to a specific fixed set of other boolean matrices
The problem is NP-hard; it is at least as hard as the biclique problem.
If you can solve the problem for a single shaped box, you can solve for all boxes by just iterating over all the boxes.  So your problem reduces to:

Given a matrix $M$ and integers $h', w'$, find a $h'\times w'$ submatrix of $M$ that is all ones, or report that none exists.

This problem is NP-hard.  In particular, if we take any undirected bipartite graph $G$ with adjacency matrix $M$, then $M$ has an all-ones $k \times k$ submatrix if and only if $G$ has a $k$-biclique.  Testing for the presence of a $k$-biclique is NP-hard, so your problem must be, too.