Every Fujitsu I have owned exhibits an increase in backlite intensity on the application of AC power. Also a decrease in backlite intensity when taken off AC. It isn't dramatic but noticeable. I'd have to say that's normal.
The other part of the problem isn't, of course. I don't think the cause can be pin pointed from the description. Whatever it maybe, it seems intermitent. It could be as simple as a lose/dirty connection/pin of the cable from the motherboard to the backlite inverter. Likewise for the conection from the backlite inverter to the backlite embedded in the LCD panel. All these parts are replacable but finding them may not be easy.
This is a somewhat difficult situation because all the effected components are in the front of the unit and you have to disassemble the entire thing to get at them. Not a task for the inexperienced or "faint-of -heart", as they say.
Some pictures showing the internals are here:
It will give you an idea of what to expect. The eleventh picture down shows the front part of the unit with the LCD panel and backlite inverter still in the case.
Hard to see, exactly what your looking at but it's the only available pictures.
At this point I don't know what to tell you because I don't know what your tolerance/ability is for self repair. The best you maybe able to do is sell it for parts and try another unit.
Third party repair could be expensive but you may want to contact an individual/dealer from this forum and get a second opinion/repair estimate. KomputerKen from JKsales MAY be able to help. He sales on Ebay (userid kenbush)and runs ads in this forum for Fujitsu tablets for sale.
His website is here:
His I-Appliance profile lists this Email address: