Hy gemisTe,
Welcome to ETO
I see you are from the US- which state?
Yes, it is correct that your monitor back light is not illuminating and that is the problem. The fact that when you shine a flashlight on the screen you can see the correct faint images, indicates that the LCD, the difficult part, is working OK.
These era hp monitors have a history of back light problems. There are some links below giving some more information. The most common problem is poor connections of the wires to the ends of the Cold Cathode Fluorescent Lamps (CCFLs). I would guess that your problem is due to a bad connection on the end of the CCFL that is discolored.
As you indicate, basic broken wires, bad connections etc aside, there are two reasons for no back light:
(1) Inverter failure
(2) Back light failure.
Inverters don't fail that often, but back lights do age and fail. The normal failure mode is a reluctance to strike and illuminate.
As there are two CCFLs behind the LCD screen, if one fails you would expect the other to still work, unless the CCFLs are connected in series, which I suspect is the case.
An inverter for a reasonably large monitor, as opposed to a laptop screen, will probably generate a 1kV semi square wave, so be careful.
You can try heating the CCFLs, with a hair dryer, to no more than 55 deg C and see if they start.
Replacement CCFLs should be available if you need them.
spec
Additional Information
(1)
https://h30434.www3.hp.com/t5/Deskt...HP-2509m-monitor-screen-flutters/td-p/1210387
(2)
(3)