Hi Thomas:
I, earlier this year, had the exact same problem that you describe with one of my BeoLab 3's in that it just all of a sudden went dead. As in no LED at all! I never overworked them and was very puzzled by this sudden failure of my primary and cherished B&O speaker set.
Since I enjoy repairing my B&O myself, I carefully took the unit apart (very easy), located the solder mounted 2.5 amp fuse and tested it with my DVM. I was able to confirm very quickly that it was open (blown). This indicated a faulty power supply board. Most likely, based on a visual inspection, the transformer.
I called down to Atlantic Systems in Hanover, Massachusetts (USA) and they explained to me that, fortunately, there is in place an exchange program whereby you can turn in the entire internals - which is referred to as the chassis - in exchange for a rebuilt one. I ended up paying approximately $300.00 USD plus shipping as opposed to approximately $1,200.00 for a new one. I installed it myself and it now works perfectly. This is a very "black-box" approach as the chassis assembly includes everything except the driver, passives and case. It is all self contained whereby the various boards are attached to a central, plastic mounting frame. Also, there is no need to remove any of the many cables from the boards themselves as the replacement will come with them attached and they want the defective one to have them left on there. If you decide to do this yourself, take photos as you go to ensure that you run your wires in exactly the same paths as things are really tightly packed in there.
If you are at all adept with a torx driver and are comfortable working on your own gear, you can remove the chassis on your own. I would start by downloading the BeoLab 3 Service Manual here on BeoWorld as it has some great drawings that will guide you along. When you pull the chassis, do remember to also remove the very small LED board as they require that too. One screw holds it to the top-inner speaker shell. I had not known this and had to ship that down to them separately.
Also, do be careful on reassembly in that you do not strip any of the screw insertion points in the case. The screws are steel and the case is aluminum. Tighten just enough to do the job. I learned this lesson in the past with plastic parts and use a very precise touch when torquing down screws. On this project, I used a torque screwdriver set on the correct setting based on the screw size, screw material and substrate material. Also, lay out a soft towel so you don't mar the soft rubberized color coat as you move forward with disassembly.
If you are not comfortable working on your own gear, you'll have to bring it or send it in to an authorized repair center and they will exchange the chassis for you.
Should you have any other questions, please feel free to ask.
Michael
Lowell, Massachusetts, USA