It's definitely not backlight problem, as the LCD should be visible in natural light, without backligth.
The ST4000+ is fairly easily taken apart. The LCD is held in place by a plastic bracket, secured by screws. Take it off, and carefully clean the contacts on the circuit board. If you are real careful, you can also clean the contacts on the LCD itself (they are invisible!) and the rubber conductor that is between the LCD and the board. Don't use WD40 or like, use alcohol!
This can help. However, if the LCD is uniformly dim, then probably there are other problems, as the above contact problems usually result in some of the segments6pixels being dim.
BTW, at the Raymarine Technical Forum Raymarine Technical Forum
they seem to be very helpful and responsive, try that.