Hey Nadine and Welcome to Apple Discussions,
First your post would probably get more views if you started a new one rather than being at the end of this one.
That said, exactly which iMac G4 do you have?
So you've done these steps from the service source?
"8. Plug the unit in, but do NOT press the power button. Using a voltmeter, check the voltage from the test point marked “Main” (see graphic above). You should get a reading of approximately 12 volts. If the reading is 12 volts, go to the next step. If you don’t get a 12 volt reading, verify that all the cables are securely connected and test the unit again. Pay special attention to the video cable.
9. Press the power switch on the computer. Using a voltmeter, check the voltage on the test point marked “12v” (see graphic above). You should get a reading of approximately 12 volts. If the reading is 12 volts, go to the next step. If you do not get a 12 volt reading, replace the main logic board.
10. Using a voltmeter, check the voltage on the test point marked “5v” (see graphic above). You should get a reading of approximately 5 volts. If the reading is 5 volts, go to the next step. If you do not get a 5 volt reading, replace the main logic board."
Note especially:
Pay special attention to the video cable.
These have been known to be a problem.
Even there isn't the 12V needed at the main board test points, does it means that the logic board is defective
Do step 15 first. If there is power on the power supply output and none at the "main" test point that points to the logic board.
I haven't done the n°14 ( i don't understand what to do).
"14. Check the connection of the video cable on the LCD flat panel, and try to power on the unit again."
This is checking the LCD connection. There's one on the logic board (careful detaches parallel to the board vs. straight up like all others. There's also another one on the back of the panel. Back has to come off for this check. There have been a few posts about this happening.
Richard