After one minute or so, the backlight was turning off, probably because of overheating.
I ordered a LCD for my MacBook A1181 and I replaced it without removing the panel. It was a little bit tricky to plug it in the inverter, but watching at pics (Fig.1) of the inverter helped a lot to know where I was going to plug it.
Buy one extra bezel mounting clip in case. I was not able to put the bezel back in place so I removed every gray mounting clip from it and clipped them on the LCD mount (Fig.2) before to clip the bezel in place. This was the only way I could do it without destroying all clips.