A powerful debugging trick I often use when some kind of plot doesn't display anything:
In your latest version of your code change
StreamPlot[w[x, y], {x, 1, 10}, {y, 1, 10}]
to
Table[w[x,y],{x,1,10},{y,1,10}]
and take a look at the result, you might need to then ask Mathematica to show you more and more output to see enough to be useful.
I see lots of
A[{someconstant,someotherconstant}]
in that and you have no definition for A that involves two items in a list, only an A that accepts two numeric arguments.
So I think the problem lies in several places where you give your A the result of vector operations.
If I make a guess that you might want this to be A[someconstant,someotherconstant] then I can try
A[Sequence@@(yourvectorexpression)]
where i have added an extra layer of () around your vector expression given to A, which should turn your vectors being given to A into a simple pair of arguments.
When I try Table on this I get a variety of warnings about 1/0 and indeterminant and complex infinities, but at least I no longer get unevaluated copies of A[...] and you might be able to tell whether the values in the resulting Table are sensible or not.
When I replace Table with StreamPlot it seems to take longer than I want to wait and this may indicate that I have misunderstood your code and even broken something.
Perhaps something in this will let you diagnose why you are not getting the plot you desire.
EDIT: Wait a minute, well actually perhaps more like ten minutes, and I actually get a StreamPlot from
StreamPlot[w[x,y],{x,1,3},{y,1,3}]
so with time you might also get a result, possibly even for 1 to 10 if you wait long enough
