Think your problem is more than just the backlight LED's as these do not draw much current and the original fault of them not lighting up would not cause a fuse to blow. Do any of the facilities work, fan speed, blow direction, air con etc, or is the unit dead at switch on. A blown fuse may be associated with a motor in the system in which case an autoelectrician is your only option. But first try taking the unit out and giving it a visual check, if the fuse is blowing there may be some signs of burning on the printed circuit boards.
Best of luck