Hi there!
A few month ago I spilled some liquid on my laptop and since then I try to repair it as good as I can.
I don't have any background in electronics and circuits except from my 1st semester of computer science.
I'm a desperate learner and people say I have excellent soldering skills when it comes to smd parts.
So I spent the last few weeks educating myself, learning about all this, and gradually repaired my laptop
so that it's working again. Just the backlight is left which doesnt work.
After a lot of googling and digging through russian and chinese forums I found the corresponding schematics and some tools to locate the parts on the board.
Now I'm left with one very tiny chip and it's surroundings.
If you like take a look:

The circuit builds a boost converter where on the left goes 12.5V in, and it should output 18 - 27V at the end of the diode if I understand everything correctly.
The maximum I measure is always 12.5V and I'm running out of ideas where to dig for the error.
I replaced the inductor, the schottky diode and the caps at the end to ensure that they are not the source for the error, which only leaves me with the IC in the middle which does the switching.
I don't really have an idea how I could debug this.
The chip is a TI LP8550 and they don't provide a full datasheet for it, but I found a datasheet for an LP8545 which looks very similar (feature wise), but is housed in a different package.
http://www.ti.com/product/lp8545But I assume they work more or less identically?
I took my multimeter and measured the pins I could locate for voltage.

(edit: of course I did my measurements when the chip was soldered to the board!)
I get the following readings:
FB: 12.5V
FSET: 0V
PWM: 0.82V
ISET: 0V
EN: 3.1V
FAULT: 0V
SW: between 0.3 and 1.6V
FILTER: 0V
VLDO/VIN: 5V
OUT1: 0V
OUT2: 0V
OUT3: 0V
OUT4: 0V
OUT5: 0V
OUT6: 0V
VSYNC: 0V
SDA: 3.3V
SCLK: 3.3V
VDDIO: 3.3V
So the chip gets 3V on it's enable pin which should be sufficient. 5V on VLDO and VIN looks good to me according to the datasheet. I don't know if it makes some difference that VDDIO is 3.3V.
On FB I would expect more than the 12V (like I said, between 18 and 27V to drive the LEDS). PWM seems to be some signal where the duty cycle will result in 0.82V.
Would it be good to look at this with an oscilloscope?
The oscillating voltage I measure on the SW pin would indicate to me that the chip is doing something.
I don't really know for what I need ISET and FSET and I have no idea how to deal with that floating FAULT pin. The datasheet says its an open drain pin. Do I need a pull up resistor to get something from that?
But as you can see, I'm running out of ideas. I'm gladful for any hint how I should proceed from here.