Hi,
Did you try adjusting the display’s “dim setting”, you didn’t say?
I have found two user manuals online for a Bose Wave radio but neither state the actual model number so here are the two “options” on how to adjust the display lighting.
[image|1745518]
[image|1745517]
(click on image to enlarge for better viewing)
If this doesn’t resolve the problem, here’s a link to the ifixit [guide|88783] guide, which may be of some help to check the connections to the display module and its’ associated components.