I doubt this is your problem, but to make sure, the polarized film goes in between the backlight and lcd. Like a sandwich. Starting from the farthest back you would have: pcb -> backlight -> polarized film -> lcd.
The way you said "even when viewed through the polarization filter" had me worried. You're not viewing the screen 'through' it as much as the light is shining through it.
Other than that, I don't know.
I did as you suggested, and that was the problem. I now have an image on the screen.
However, when I reassemble the Gameboy, more problems arise. Sometimes I don't have sound, and sometimes there's no picture. When I take it apart again it works normally. Am I not putting this thing back together correctly?
I really appreciate your help!
EDIT: I've succeeded! The problem seemed to be the backlight wires being slightly beneath the button silicones. After reassembling it the Gameboy worked fine on AC power, but for some reason not on battery power. I changed the batteries and now it works well. This was my first Gameboy mod, so hopefully it holds together. Thanks for your suggestion stargazer.