I'll go looking for a description of inverter board you mentioned and see if it is something I can do or if I have to have a repair facility do it.
P.S. My Power supply is almost new and both batteries still provide power for an average of 2 hours so I don't think power is the problem.
I'd recommend taking it to a mac repair shop - while the TiBooks from 400 to 1GHz all look pretty much the same, the insides varied all over the place, far more than I'm familiar with! Various parts are incompatible between models.
Power may also be a bit iffy deeper in the machine than the battery and the external power supply. The power from those goes through a DC-DC board, is controlled by a power management unit, is split between logic board, HD and Optical drive, and also goes to the screen's inverter board. Any point along there could have issues giving power related problems, even if the CPU is getting constant clean power from both Battery and the external power supply.
dana