If it works on an external monitor - and you've already replaced the screen anyway - then you've already got your answer.
The fact that is still doesn't work immediately after post on an external monitor and only shows up once the system boots into Windows shows that your hardware is not properly working - a normal monitor - even an external one - shows a display right after the system is turned on.
Backlight/inverter issues would've been covered when you got the screen replaced.
Does it behave the same way regardless of power source? Try turning your laptop on with just the battery as the power source and just the ac adapter as your power source.
If it behaves the same way, you can rule out power issues to the monitor.
Then - as I suspect the problem is - you'll have to replace the graphics card, or if it's integrated onto the motherboard, then you'll have to replace the motherboard.
Windows doesn't control the output of the monitor, it only receives it and can tweak the way it looks with user input. Going down that road won't do you any good.
Edited by dudeage, 13 April 2015 - 09:38 AM.