Yes, if the backlight is on, then the inverter is working.
Sounds like you may have a power issue. You will have to check voltages at the power supply and also at the LCD with a multimeter. My guess is that you lost 5V on the Power Supply, so the CPU is not getting powered. But you will need to verify by measuring first.
You can download the service manual from this thread:
viewtopic.php?f=17&t=109567Many of the links there are dead, look for the post by Lampdog for a working link.