Unfortunately, I think replacing one or the other is the only way to determine that. However, the cable is more likely the culprit, so I'd say that's a better place to start than the inverter. Actually, the screen itself is often bad in this situation...I hate to say it, but due to the difficulty getting PowerBook screen casings apart, I generally just replace the whole thing if possible -- screen with casing, hinge, and cabling. If you can find one cheap enough on eBay or whatever, you'll likely be saving yourself a lot of trouble and aggravation, although pulling it apart and granularly testing the components is possible.
Also, I'm assuming you can see the image but the backlight is dead. If there is no image at all, testing the external video is the next step. Good luck!