Welcome to the Intel® Embedded Community. Let's start by confirming that your are working on an embedded system rather than a consumer-class laptop. Can you say anything about your application?
In the meantime, it sounds like you've already tried one approach which probably means that you have some relevant docs. Just in case you don't already have it, let me give you a link to the 945 datasheet. I have to tell you that I have no technical knowledge on this chipset but I did search this doc and there are several references to controlling the backlight in addition to the LBB register that you tried.
Let's see if someone out there in the community can help you.