The iMac g4 had some problems with scuffed cables inside the neck, but the inverter or the ccfl tubes are old - so they can also make some trouble.
i would first check the cables inside the nack - but it's not easy to open it. please read more about the whole disassembling process on: http://dremmeljunkie.blogspot.com - this guy made some heavy modding with his iMacs - but you only need the part with the neck ;-)