Minecraft – How come the trash isn’t being taken out

Routers are, in my experience, your best bet here, you can configure one router to pull the scrap out (set the router to extract from a side), and one router to insert the required items (insert into top).

This way you need one Export/Level emitter per type, up to a maximum of 4 per router (technically you can add more per router, but it's messy). If you want more than 4 types of items you can add another router set to insert at top without problems.

This setup would also be easier to expand as you would just need to run IC2 power further and add the block next to the existing system. (http://imgur.com/a/wdnDY)

Two options:

First, use buildcraft Gates, that is what they where designed for!

Have one gate detecting if there is space in the destination inventory, have a 2nd aurtatic gate connected by a pipe signal pulling out of the first chest.

A 2nd option, put a turtle between the two chests, you already said you have computer craft, just put a turtle between the two chests and have this simple program run on startup. It sucks 16 stacks of items from the below chest and tries to place it in the above chest.

function suckItems()
  for slot = 1, 16 do
    turtle.select(slot)
    turtle.suckDown()
  end
end

function dropItems()
  for slot = 1, 16 do
    turtle.select(slot)
    turtle.dropUp()
  end
end

while(true) do
  suckItems()
  dropItems()
  os.Sleep(1) --This may be unnecessary
end

for fastest speed I am assuming your layout is

[X] = Chest 2
[T] = Turtle
[X] = Chest 1  (looking at from the front)

You could have it horizontal but you would need to make the turtle turn every time