Chosen Solution
I have recently bought a faulty Samsung Syncmaster F2380 monitor in hope of fixing it and using it for personal purposes. The device used to work for a few seconds before turning off the backlight until pressing the power button. After opening up the device I noticed one cable of the CCFL backlight had burnt at the solder point on the CCFL tube. After resoldering the connections to the tubes and checking everything else I reassembled the whole thing back together. Unfortunately now the monitor turns its backlights off when plugging in a signal cable (e.g. VGA or DVI), but remains on when not plugging one in (except it outputs the expected “Check signal cable” because nothing is plugged it) I have also checked all capacitors on the main power board, as the CCFL lamps connect directly to it. I do not know how to check whether the CCFL Lamps are working or where the issue lies, but its just strange that the backlights only turn off when plugging in a signal cable. I would get an image for a few seconds, then the backlights would turn off. Perhaps the device turns on additional backlight lamps when it receives a signal? I will open it up again sometime, and check which lamps actually turn on or not when plugging in a signal cable. I really dont know what things to check next, so I would really appreciate help on this topic (especially as many others are having this issue as well)
I believe I have figured it out. Upon inspecting the components even closer again after Conor Bailey above suggested to check for burned caps or similar, I noticed a slight yellow taint to the text ontop of the backlight inverter (as seen on the images below). After desoldering the transformer spool and flipping it around, I could immediately see a part of the spool being covered with black material and that it was a bit burnt. It appears as if the inverter spool somehow got overloaded and burnt its wires at one winding. As the transformer is directly connected to the backlight ports (by tracing the pcb from the transformer), this explains why they turn off as soon as more load is running through (exactly what happens when a signal cable is plugged in -> the backlights need more power and additional backlights get turned on) If you have this or a similar issue, make sure to check the backlight inverter transformer, as they commonly get a burnout on their bottom side!
Notice how the windings of the spool look clean on the lower part of the picture, while one winding segment (where my tweezers point to) at the top part of the picture is completely burnt. Checking the resistances confirms that indeed electricity can’t get through that part of the spool. The extreme heat the transformer gives off while running also confirms the above, as there is much greater resistance.
The next step is to find a fitting replacement part, oh well!