Unfortunately, having a bright external display does not rule the logic board out as being a possible fault. the external display has its own power supply and backlight driver. the only data being sent from the computer is image data. So the fact that the external display is bright just indicates that your test monitor is working.
As for the fault with your laptop, can you please confirm a few things?
In the display preferences of the mac, can you see the brightness adjusting bar, or is it not present?
The possible causes of the fault are:
Logic Board.
Inverter Board.
LCD panel.
The only reason i'd suspect the cable is if it comes and goes, or if its affected by movement, or you have no backlight at all.
if its just dim, i'd look to trace the other items.
The logic board provides just voltage. so as long as the voltage is being provided as it should, then it wont be at fault. There is a backlight fuse on the board that protects against shorts or blowouts, but as you are seeing some backlight, that would indicate that the fuse hasn't blown.
I'd look to suspect that you've been sold a dodgy LCD initially, as that is the most universally accepted item. The inverter boards are made specifically for this range of mac, so are less likely to be altered or made by 3rd party companies, but LCDs are often built and adjusted by refurbishing centres.
Is there a white label on the back of the LCD panel indicating a model number of any kind? that early model of MacBook was usually shipped with one of 4 LCD brands, but the model number will help confirm if its actually compatible with your machine type.