Boots fine, no screen

I have the 1.83GHz Core Duo 17" iMac. When turning it on it will boot, chime, fan spin, the LED will light up (the iSight light turned on also), but the screen never illuminates. With the keyboard plugged in, I can push caps lock and see the light go on and off, and if I wait about 20 seconds, enough for it to theoretically get to the desktop, I can push the volume up and down keys and hear it raise and lower the volume. Pressing the power button once will seemingly put it into sleep mode, as the LED will pulse. It seems it's working fine, but the screen is totally dead - I can't see anything with a flashlight. What would be the proper thing to replace here, the inverter, or the display itself?

Obviously it's an 11 year old computer, but if I could get it working for my parents that would be cool. Thanks!