To find out if the inverter or bulb are the problem, turn the computer on. Use a flashlight or some other light source on the screen to see if you can see output on it. If so, but it's just dark then you may well just ahve a problem withthe inverter or the bulb.
If you don't see anything, then it could be something as simple as a bad connection or somthing as bad as a bad graphics cards (which in most cases will require a new mother board to fix). Try connecting an extreanl monitor and seeing if you can get output there. You may have to play around with some combination of keystrokes to get display on the monitor (in both of my tecra's it's Fn-F5)