This is an exercice is Rolf Niedermeier's book "Invitation to fixed-parameter algorithms", Chapter 13.
Show that the following problem is W-hard: Steiner Tree in Graphs with respect to the parameter "number of non-terminal vertices".
The way I understand it, if there are most $k$ non-terminal vertices, then this doesn't help in solving the Steiner problem in time $f(k)n^c$.
The objective is to find the minimum number of edges connecting terminal vertices (while some vertices are non-terminal). I can't find a reduction however. I am convinced that the parameter $k$ being number of included non-terminal vertices in a solution makes it W-hard. But if $k$ is the number of existing non-terminal vertices, I don't know. Proof ideas or references will be appreciated.