I would make a selection of all screens, using plain rectangular selection -
If that is too complicated to do in a single pass, since combining selections can be gone in a single wrong click, you could use the "quick mask" (edit the seletction using arbitrary painting tools by clicking on the square icon to the right of the horizontal scrolling bar on the image window). Anyway, since the screens are rectangular with no perspective, the rect-select tool is the ideal to use there.
Once the selection is made, the tool of choice there is
colors->color to alpha. Save the selection to a channel
Select->Save to Channel, then, select by color, use selection intersection, click on the gray area, and use color-to-alpha selecting the gray shade. For the white squares, select the white color on all the image, combine with the saved-screen selection using "intersection", and color to alpha again.
This won't preserve the glare over the white squares - since its color match the squares bellow. You could try to retouch the glare by using the clone tool afterwards.