Dana, your diagnosis seems feasible as the longer I try to run the PB the shorter the screen displays anything. If I wait several minutes, then reboot, the display will work long enough to maybe make it through the login. After that, if I close the PB, wait for the sleep indicator light to come on and reopen it will display for a few seconds or just flash the screen.
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.