My family loves the g4 iMac.  Moving the screen every which way for five different people, and for when a parent works with a child at the iMac has been perfect.  We really do not want to give up the form factor.  So, to me, it looks like a Mac Mini could fit inside the dome of the iMac with some sort of MOD.  All forums and notes I have read have indicated that there does not seem to be a way to connect the iMac's flat-panel screen to the mini.  But why not wire-up (connect) whatever wires come out of the screen (or swival arm) to a normal Mac monitor connector.  Wouldn't such an action be similar to someone accidentally smashing the ADC or VGA (or whatever) connector on their external screen, and simply cutting that defective end off, and wiring on a new one?  I'm no expert, but I have always followed all detailed directions shown to me form places like xlr8yourmac, or Apple Manuals.  Why are the wires that come out of the iMac swing arm such a puzzle to everyone?

Its not specific to the iMac. Everything with a built in LCD has different pinouts at the logic board end. In a standalone LCD display, there is a controller board which converts VGA or DVI to run the LCD panel it has in it. You would need to know the pinouts of the LCD you have in order to stand a chance at this working. I suspect if you know what they are they are not too dissimilar to DVI, but you really need to know what you are doing.

You could attach a 23" cinema display (old style) with an adaptor and put the mini the case.  That would be cool.

War is right.  You need to know what you are doing.  It is possible, but you need to figure out how to power the lcd too.

"In a standalone LCD display, there is a controller board which converts VGA or DVI to run the LCD panel it has in it."

So, what  your are saying, is that there would be no controller board IN the G4 iMac Flatpanel?  I'm just trying to get a handle on this.  So, in the monitors that one buys off the shelf, there is a connector, but the display has some sort of "controller board" in it to make it all work?  If I understand that right, then the G4 iMac dospaly had not controller board built into it.  Hmmmm...

Let me know if I'm getting this right.

There is a controller somewhere in there, but it is built directly onto the mobo(i think).  This is often referred to as the "Holy Grail".  Most people want to do a similar mod in order to use a notebook lcd as a stand-alone screen.  I guess the LCDs in G4 Imacs are built in a similar fasion.
You could buy an LCD the right size (15 or 17"?)and rebuild it in the Imac screen housing.... if you can find one that fits.  Then you will have totally gutted the Imac... It seems like the least risky thing to do would be to buy a nice swing arm for a new LCD.  But what fun would that be? 
check these links for some more info
http://www.macmod.com/component/option,com_smf/Itemid,222/topic,1347.msg9424#msg9424
http://www.applefritter.com/holygrail

Yes, in laptops and iMacs, the controller board is skipped because it doesn't have to convert the signal to a standard (DVI) pinout. The graphics chips do the job of the controller. Thats why you can run the LCD from a 14" iBook in a 12". They have the same GPU, and the same connector. As long as you have the display cable that matches the display. They are all the same at the logic board end.

If you are considering replacing the panel with a DVI or VGA one, your problem will be the neck. The neck of the iMac G4 has a huge spring in it. If you undo it, it will literally explode. Apple engineers are not permitted to do this. If you break the end of the iMac display or inverter cable, you have to replace the whole neck. I have never taken one apart, but I have put one back together. It took two of us, and I'm pretty strong. You would really have to run cables outside the neck.

I have no idea how to do this but i'm 100% sure that its possible but it will for sure be tricky.  I suggest a lot of research first.