LED Strips are parrallel, if you put 12v in one side theoretically you should get 12v out the other side, however in reality there will be a slight voltage drop over 5 meters.
If you connect three 12v strips in series you should be able to light the led strips up without damaging anything.
When i did this on my own TV i didnt trust the existing powersource because as Dampmaskin said theres a good chance that whatever caused your LEDs to die is still happening. I just ran it off a separate 12v power supply. What i didn't take into account was the brightness of my 12v strip was different to the factory LEDs and even when viewed through the factory diffuser there were obvious points of light so more diffusal was necessary.
As someone who has done this before i can tell you that Richard Chambers has it right, get it fixed under professionally preferably under warranty.