A picture or more detailed component description (color, numbers on it and the board...) and it's location on the board would be helpful to determine if it might help your backlight prob. (I toasted an smt fuse (F1) on one of my iO's and had to replace it (I had no backlight either))
At any rate, you can also use conductive epoxy, available at electronics shops, in place of solder. Just use a tiny bit on the loose component in case you need to remove it, making sure that you dont inadvertantly trace to any other components with the epoxy. It is kinda sticky and somewhat messy to work with.
Sounds like you have not soldered before, if so, IMHO, I wouldn't touch the board with an iron. Not a great place to practice.