It seems as though there is a backlight problem but whether this is in the LCD panel, the video cable or cable connector at either end (loose?) or the motherboard would have to be determined first.
Looking at the image you posted it may be not where you indicated but perhaps the wires that are connected to those pins. The last wire looks as though it is broken but it may just be the picture. Also unless what you have shown are pins 38 & 39 it doesn’t apply to the backlights. The pin numbering should be printed on the motherboard. 1 at one end and 40 at the other end of the connector on the board
(click on image to enlarge for better viewing)
Without tools or knowledge this will be more difficult for you to do yourself.
Here’s an image taken from p.24 of the schematics for the laptop’s motherboard, showing how the backlight power is connected to pins 38 & 39 on the video cable connector.
With the laptop turned on the power is always there. The backlights are turned on and off in the LCD display panel by a signal voltage being present or not on pin 9. (disp on).
(click on image to enlarge for better viewing).
If the power is not there then there is a problem on the motherboard with the backlight power supply circuit.
If the power is there, turn off the laptop and then gain access to the LCD panel so that you can disconnect the video cable from the panel (and the motherboard) and use an Ohmmeter to check for continuity of the cable’s backlight power wires and the Display On wire from end to end.
Here’s the service manual. Go to p.103 to view the necessary pre-requisite steps and then the procedure to remove the display assembly.
If the cable is OK then the problem is in the LCD panel.
It may be easier to source a replacement panel than to replace the LEDs. Usually the part number can be found printed on the back of the panel somewhere. Search online using the part number only to find suppliers.
If doing all this seems too daunting, contact a reputable, professional laptop repair service and ask for a quote.