you can try my custom brightness first, pretty sure this will not solve the problem but it is just to be sure before you dismantle your phone.

Else:
You can replace the screen.

or

You can take the screen of and check if there is any "dirt" in the connection between the screen and mainboard (ribbon cable & connector)


The backlight in the screen is a LED and normally there is no way in hell it breaks before the LCD/Phone
Other then that if you are very unlucky then some power control transistor/mosfet on the mainboard is fried and this would be next to impossible to fix

But i will first recommend that you try the custom brightness
Then check the ribbon cable if it is just a little loose in the connector or any dirt on it, i have had the same problem with an N95 and here it was the ribbon cable that has a bad connection, so i clean it up and the N95 works fine.