Three things are in question here,one, the FL Tube (the light IN the display itself), two, the FL Inverter, three, the motherboard. The fact that the screen lights at all tells us its probably NOT the FL Tube, indicating the screen itself is probably OK. Now we still have an issue about which two is the culprit, you can put a voltmeter on the FL TUBE side of the inverter, set to handle about 600V AC, if you get a steady reading then it will be in fact the screen, if you get zero, or a sporratic reading then youve eliminated the screen for sure and need to test the DC side coming from the board, typically between 5 and 10 volts. If you get a steady reading, the inverter is probably bad, especially if you get steady on that side, and zero or sporratic on the fl tube (screen side). If you get a zero reading either your not getting good contact, i know those small contacts can be hard to get, or the board just isnt giving the inverter anything. Also check cables, any of them could be loose/pinched/bad causing this, and one other slim possibility is something is causing the "sleep button" to stick or short when its not supposed to making the screen flicker on and off, and eventually off completely. Let us know what happens with this, id like to know what the issue is, or if you get more info maybe i can help further.