I have a Blackburn x3 light system that went completely dead as well. I decided to crack open the black box and see what I could find! Here's the good news:
The battery pack is two halves held together by four screws. The screws are hidden under plastic caps on the side where the charger and lamp are plugged into. Remove the four screws which I think are 2 mm hex head. Pull the unit apart. You will find a circuit board, and five A cell NiMH batteries bundled together. Initially, I thought I would go buy some new batteries and solder them together to make a new battery pack. These batteries are available with solder tabs for about 4-7 bucks a pop, depending on where you get them. THEN, I noticed that there was another little 3 volt button cell (Panasonic CR 2025) located on the circuit board. I just happened to have one of these batteries handy. I inserted the new button cell into the holder and noted that the charge light began flashing red when I plugged in the charger! I left it on the charger for about ten minutes and what do you know, the headlamp turned on! I charged it overnight, and now the light will run for it's normal 3.5 hours at max intensity. I guess the 3V button cell powers the brain that controls the charging and operation of the light. This fix cost me four bucks and saved me unknown quantities of dough on a new light or battery pack. If the button cell does not do the trick, I suppose you could buy the A cell NiMH batteries and make yourself a new battery pack, it would be relatively easy if you know how to solder.

Remember: you can fix anything, you just can't fix everything!

I hope this works for you!

John