If the motherboard is model number NM-F351 (printed on the board), below is a composite image (whole board - top and zoomed in section of board - bottom) from the NM-F351 boardview file showing the location of the F1 backlight fuse (fuse type # 3A_32V_0497003PKRHF).
Run the LCD self test and check if it works OK just in case it is not a backlight power supply problem but something else e.g. problem with the backlight enable circuit on the motherboard (connects to pin 49 EDP connector)
If the test proves no good, here's an image of the schematic showing the backlight power supply through the fuse to pins1-3 on the EDP connector on the motherboard.
With the laptop turned on etc, check what voltage is on those pins.
The feed states V9B+ so maybe it should measure 9V DC but as to why so many capacitors are sitting on the supply line I don't know. Maybe need to smooth out the supply.
If one of the other capacitors on the line i.e. C19, C10, C307, C314 & C315 was faulty and shunting the voltage to earth this may be the reason for it being faint
There may be a lot of current flowing (Amps) so try not to short the pins to anything else when testing for the voltage.
If the correct voltage is there you may have to disassemble the display unit and check what the voltage is on pins 1-3 at the other end of the EDP cable where it plugs into the LCD panel, in case the cable has been damaged where it passes through the hinge to get from the motherboard to the lid.
If the voltage at the LCD panel is OK then most probably it's a faulty panel which would have to be replaced.
The fuse you linked may be a bit small in that it may not bridge the distance between the two soldering point on the motherboard.
Here's a link that shows the common smd package sizes that may help.
You have linked a fuse (which has the correct rating 3A/32V) with a package size of 0402 (see link).
The 0497 size shown for the part is a non standard size so it may be easier to get one a fuse that's slightly longer so as to bridge the gap but not too wide as not to touch any other components on the sides (or the ends either)
@jayeff looks to me like the white (far right vertical component) is F1 and the middle component that looks smushed ;-) (missing) would be C310 which is a 0.1Β΅F 25V capacitor in a 0402 and is part of the LEDVDD circuitry right next to F1 :-)
2 
421 
1,6ΠΊ 
