linkI've done some more digging and it seems that you may not be completely out of luck after all.
The official B&O marketing video shows some details that are very interesting.
Login to view image
This is the main board, ie. the motherboard of the unit and it is part of the display module. The bad thing about that is that the official replacement display module from B&O is probably prohibitively expensive. The good thing is that it shows the flex cable connector, which is a potential source of a malfunctioning digitizer (that is the thing that provides touchscreen functionality).
Beo6 uses a capacitive touchscreen and that is probably an integral part of the screen (as opposed to the resistive sytem used in Beo5). Since touch functionality is completely absent there are only 2 primary error sources: a contact problem between screen and motherboard or a damaged touch controller (the latter is possible but unlikely). Similarly, a complete malfunction of the transparent touch layers on the screen is rather unlikely.
So, if you're lucky, a simple unplugging and replugging of the flex cable might fix the whole problem. You only have to figure out how to disassemble the display module. I'd guess it works in a similar way as modern mobile phones. There could be some tiny screws somewhere at the base of the display and once removed you just need a pry tool to separate the cover from the screen.
In the Beo5 service manual I noticed that B&O used a standard TFT screen from Samsung. That's a standard product you might get off the internet. So if there's something wrong with the TFT screen + touchscreen layer, you might actually get a new one for, I don't know, say 50 bucks? That might be worth it. Just make sure you find a model number on the screen unit when the display module is disassembled.