For me, every computer I've played on has allowed me to see my coords in Minecraft, and If I hold down F3 and a button, it uses the keybinds. But with this ones, I'll do FN+F3, and It doesn't show my coords, instead, it treats me like I'm holding the button down (Pressing A Reloads chunks, Pressing D Resets chat), and It never works!
In my experience, you usually just need to tap F3 to toggle the coordinates, not hold it down. I am also aware that on some computers, the use of FN is inverted, so you have to press just F3 to do Minecraft stuff, and the laptop functions (brightness etc.) can be used by adding the FN key.
If that doesn't work, have you tried posting in Mojang's forums? They might be able to give better info.