August 4th, 2008 | 
Author:
from what you describe, it very well could be the inverter, hard to say, especially since i have never seen it.
HERE is how to do the work yourself.
Here is the screen that should go with your laptop. it will contain the backlight inside of it. it does not come with an inverter.
TOSHIBA SATELLITE A55-S106 15" XGA LCD Screen Matte A+
here is the inverter.
Toshiba Satellite A50/A55 Inverter
you can also just try and buy a used working laptop thats the same make and model and just swap your hard drives and add your existing memory.
Used Toshiba Satellite A55-S1064
this is the backlight, it is very dangerous and very VERY fragile, it contains mercury which can cause cancer. it is thinner than half of a pencil and almost nobody replaces them because they are usually sandwiched between LCD wafers, very difficult to replace.
If you still need assistance, your cheapest method may be to use one of the many companies on eBay that claim to fix it for super cheap, like this one:
LCD Repair TOSHIBA SATELLITE A35 A40 A45 A55
