No backlight + no keyboard backlight implies fuse problem? I have a MacBook Air 13" mid 2011.

I have had display problems, so I changed the backlight fuse. After that, there is still no display. The computer works fine otherwise, I can turn it on and hear sounds. 

As of now I am wondering whether I soldered wrong, or whether the problem is with the backlight itself.

I also noticed that there is no keyboard backlight. Even if I hit the keyboard backlight keys, it doesn't light up.

I was wondering whether that means that my soldering is wrong, or not. Is the backlight fuse also "protecting" the keyboard backlight ?
If your backlight fuse was defective it might have damaged the backlight of the display. In official repairs an authorized service provider would replace the logic board AND display when the fuse was defective.