Can you explain what "duplicated images" means in more detail? It does not sound like a failure that graphics hardware or LCD would sustain.
If you can used it in some capacity, go to System Preferences Universal Access pane Seeing tab, and make sure it is not one of those settings that got enabled by mistake.
If you can, also enable "Screen Sharing" in System Preferences Sharing pane. Then, from that other Mac that is connected via Ethernet, you may be able to "remote control" the Mac with the display issue and do some more troubleshooting. To do this, on the "other" Mac, open a Finder window. Find the iMac under SHARED (in the sidebar), and select it. Over to the right, click the Share Screen button (and log in). If it's a hardware issue, the iMac's screen should appear normal when viewed from the other Mac using Screen Sharing. If it still looks messed up, then it's not a hardware issue but something related to software or settings.
Another way to confim it's a hardware issue is to start up from your Mac OS X installation disc. Insert disc and restart with the C key held down. If it's a software or settings issue, it should look normal when starting up from a different system. If it still looks messed up, then it is probably a hardware issue.
Kenichi... In the first place, thanks for your interest. I will try to do has you say, and tell you, in case your interested, what finally was the problem.
When I described what happend to the image, I was no accurate. Soppouse you just started your iMac. For a short it it performs normally, but all of a sudden, as you move the mouse arrow throw the screen, it seems as if the image of the finder would follow the arrow, leaving traces of it and pixelating the screen image.
I'll keep you informed .
OK, that sounds more like a possible graphics hardware issue.
If you have not already, reset PRAM
and if that does not help, also reset SMC (power management)
When you reconnect it to power, if you have been using a power strip of some type, try a direct connection to a wall outlet by itself (at least initially). Power it up with nothing but the power cord connected, and add only standard keyboard and mouse. Use it that way for a while to see if there is improvement.
It might be related to heat, so inspect at the air intake vents along the bottom edge of the iMac to make sure there is no accumulation of dust blocking airflow. That may be why the problem does not occur immediately, but starts to happen after a short time.