My old Vostro 1400 display goes black shortly after startup. External monitor works fine, and the image is visible on the screen if I shine a bright light on it. So, I conclude that either the lamp driver or the bulb is bad, am going to try repairing but don't know where to get these parts. Options for my computers tag don't show these parts.
You'd have to try EBay - - or replace both the screen and the inverter together, which is likely the best option.
There was once a time when replacing the bulb or inverter made economic sense because of the cost of LCD panels -- it no longer does. You can easily replace the screen and inverter for well under $100.