There's another possibility.
If you shine a bright light onto the screen can you see a (very dim) image of whatever software is running? It will be dim because you're relying on reflected light from the LCD instead of transmitted light. If so then the failure is either the backlight or the inverter board that powers the backlight. I include the wiring for these when I say this.
If it's the inverter then it can be a cheap fix - replace the board & away you go. My old Twinhead PII's inverter board costs ~15 quid.
If it's the fluoro. backlight then it can get rather more expensive to obtain a suitable replacement light. Presuming that it's possible to separate the backlight from the LCD screen without damaging the whole thing.