The inverter board is the part which needs to be replaced, a search finds them running about $130 dollars.
If you want an Apple ADC display, it may be less expensive and less work to find a replacement display on eBay or Craigslist. You might even find a larger Apple display for the cost of the repair parts.
You could also consider buying a new LCD - there are many good 3rd party options in the $130 range, and a new device, with newer technology, will probably outlast your G5...
I found an excellent take-apart at: http://mac-guild.org/display-repair.html
The class-action settlement probably no longer applies, as this model has long since been put on the obsolete list, BTW.
Good Luck!