I have converted the 20" iMac G4 to an LCD which can be hooked up to any VGA or DVI computer through the base. I did this by replacing the existing LCD with one that hooks up through a standard LVDS connection and wiring it to the inverter power source and LCD controller board through the base.

I am attempting to do a similar mod to the 17" iMac G4, but to add a resistive touch screen as well. I am detailing the process at:

http://dremmeljunkie.blogspot.com/

It's amazing realizing that I posted this almost 2 years ago. This is no longer how I would approach this mod at all - in fact I disassembled this particular mod as a result of safety concerns. For the 20" iMac mod you can use the native, unaltered frame, LCD, and inverter. You need to alter some of the wires in the neck, but it is compatible with the controller board from the aluminum 20" apple cinema display. Thus, you can turn your iMac into an external monitor or a modernized all-in-one. But, the conversion to LVDS is no longer something I can recommend doing.

http://dremmeljunkie.blogspot.com/

I need a logic board for the 20" Cinema Display A1081.
Would you happen to have a used one laying around?

I do not have an extra logic board. But if you want it for this mod, you do not need it. I have a different method that requires no alteration of either the LCD or the neck. Nor does it require any components from a cinema display or other monitor.

I am currently putting together a Sandy Bridge based 20" iMac G4 All-In-One Mod based n this new approach.

See this Guide for details if interested:
http://dremmeljunkie.blogspot.com/2011/11/all-in-one-20-imac-g4-genuine-tmds-to.html