Problem with displaying any picture at all.

Did your testing include utilizing a second display and adapter to see
how a mirrored output of the video would appear; to be sure this item
is isolated to the wiring from the circuit boards to the attached LCD?

There are components within the border of the iMac G4's display which
may affect the image as they wear out and/or fail. The inverter, is one
item that is in the panel along with the backlight and liquid crystal layer.
Removing or replacing the wire harness between these components,
the computer base and LCD panel, is a bit of work. This topic has been
addressed in these forums at one time or another; and a few owners
who contribute here have experience taking these apart. In the past,
getting a known-good display with chrome arm and harness, from an-
other iMac (perhaps one with logic board failure) and combine two,
was an answer when the complete display & arm were known good;
as this saved a fair amount of work on the upper end. Still, taking the
lower orb shape apart is a significant task; to have it work right again.

The cabling could be faulty; the inverter could be. And there may be
yet another associated component failing which produces symptoms.

Taking apart the chrome arm may not be such a good idea; I've seen
the expanded view of one taken apart by a metal cutting saw, and it
has a big spring inside, and a bit of tension. There also are friction pad
parts inside that loose their ability to hold up the panel, so some owners
sought to replace those to varying degrees of trouble.

There should be a few step-by-step instructions. One of the contributors
to the iMac G4 forums here was Mr Totes; one of his web pages had a
few images of take-aparts he'd done. Other sites had basic stuff, such
as replacing optical drive and hard disk drives, thermal paste, RAM, etc.

If you were able to see the correct system images from a second display
via the VGA adapter cable, in mirror mode, the attached unit certainly is
suspect; and the computer is probably repairable. Otherwise, there is a
video component on the logic board not considered a separate part; and
if that fails, the usual fix is to get a reman logic board or another iMac.

Have fun, whichever way it goes.
Good luck & happy computing! 🙂

A mini-VGA adapter from an iBook G4 is likely same as the one for the iMac G4; and the product
is also still available after a thorough search of the online Apple Store. {I bought a spare one at
a charity thrift store for $2. USD a few weeks ago, and a second one for a different portable Mac
for the same price. Both look like new, and have protective caps over the connectors.}

{So, now I have extras. If not for the expanse of the Arctic Ocean, I could rush one over!}

Almost anyone with an iBook G4 or white G3 that usually shipped with the mini-VGA adapter
and kept the accessories, should have one sitting around. New, they are over $12. USD.

That is one of the best ways to test the graphic processor's output, since you by-pass the
cabling to the main display and see the output from the processor ahead of all that. And
these symptoms of display issue have been often due to failed video circuits on logicboard.

With an external display so you may see the actual computer's system, (if that much is good)
you could run the Apple Hardware Test in a loop or other option to test the video & more.

So, I guess I'm fresh out of ideas most likely to narrow this field down. If a second display
shows the same symptoms, then the video circuit usually associated with the logicboard
is the problem, and often the whole board had been replaced in a service, with a reman.

{Some of the searches for related problems in discussions suggest the wires may be bad
or the connections could be loose; or the video component bad on the logic board. A few
suggested perhaps a bad LCD with the color shift; but no data to it suggests cabling. If
the computer can be run in Target Disk Mode, and the display appears normal to show
that FW image icon, the panel may be fine. But wires can flex and be failing.}

re: see 'imac G4 pink screen of death' and associated replies:
http://discussions.apple.com/thread.jspa?messageID=1739744

Good luck & happy computing! 🙂

{ edited 2x }

The troubleshooting of connectors or broken wires, was part of the reason for the
link, belatedly added to the above post, regarding screen symptoms; pink or not.

The diagnostic and troubleshooting services of a pro tech shop would certainly
supersede most anything a layperson could perform at home, given these shops
sometimes have a good budget; and also have a way to pay for better toys.

The mini-VGA adapter could have saved you hours, re: in moving the logic board(s.)
And cleaning off/re-applying thermal paste, torquing screws... testing connectors.

There is a fair chance, as you suspected, the wiring harness in the chrome arm may
be the cause of the issue in the one computer's display appearance symptoms. In
the original repair situation, the chrome arm and its wiring harness were replaced
together when it was an AppleCare authorized repair, as to assure no issue remained.
(A first-hand experience with fourth rate repair under AppleCare; where the shop also
damaged the logic board and I spent six months and 3,000 miles getting it all fixed.)

At times, I've been guilty of understanding way too much.
And try to not show it.

Good luck & happy computing! 🙂

Sadly, I don't know much about some of the mysterious stuff inside these
magic boxes. If you can contact mrtotes, he may have some ideas based
on his hands-on experience.

Best wishes & regards.
Good luck & happy computing! 🙂