Most probably it's the background lamp that ist broken. This lamp lights the lcd display from behind and when it's broken you don't see anything (obvious). I have a pair of BeoLab 5000 (the bigger brother of the 3000s) and I have the same problem. If you shine with a pocketlamp directly on the dislay you maybe can see that the display still works but ist just not lit...
Maybe a B&O dealer can help you with that. If not, try some electro-technics freak store, perhaps they have the intuition to be able to repair it.
BeoVision MX 8000 Dolby, BeoCord V8000, DVD1, BeoCenter 9300, 2 Stück BeoSound Ouverture
2 Paar BeoLab Penta III, 2 Paar BeoLab 5000, BeoLab 2, BeoCom 2000, EarSet 2, 4 x LC2, 3 x Beo4, BeoLink Converter