That's what I like about the Dell laptops we have. Easy to get parts and easy to work on. Replaced the screen and keyboard on them no trouble at all. Unlike Apple crap which you can't easily even open let alone get parts for

Well, I don't know if toshiba satellites are easy to take a part. 

The inverter is a separate part, usually with few pins connector that have :

 - Vin voltage (+ - ) Normally somewhere around 10..15V, not 18V

 - Enable signal (on/off) - i think it is at logic level (3.3 or 5V), polarity (e.g. 0V=on or 5V=on) can vary

 - PWM dimming signal, voltage and default value (when left open) can vary

Few laptops like Thinkpads have some other "laptop" stuff integrated on the inverter board, and there is a possibility that it would need some more signals to switch on. But if you got one of them, you can get another simple inverter and use the CCFL with that



Also. 9V batteries have draconic internal resistance which may make it not work. You might get better results with using the 2 batteries in parallel (also, you won't exceed the inverters voltage rating in the no current draw periods)

At the very least, bypass the input power to the inverter with a low ESR capacitor

Maybe a small 12v lead acid battery will work with the inverter. I wonder if I can feed the PWM signal input with 3v from 2x AA batteries, so the inverter will think that is a 100% duty cycle.

If you just want to see if a fluro tube will light up you can use an insulation resistance tester set to 1000V and it should just light up. If you want to make it light up to its rated brightness then this will definitely not work.