Thanks again osxrules!
It worked very fine.
Now I have no problem with my FCP4 with New iMac 20"
1. Go into the "applications" folder, find the file "final cut pro", Open the Package Contents of the file by holding the [control] key (or "right click") clicking on the icon and selecting "Show Package Contents".
2. Enter the "contents" folder, then edit the "info.plist" file with a text editor, find the following sections Required IO PCI Device.
And change to PCI.
-Original Section Entries:
<key>AELMinimumRAMSize</key>
<string>256</string>
<key>AELRequiredCPUType</key>
<string>G4</string>
<key>AELMinimumCPUSpeedSingle</key>
<string>350</string>
<key>AELRequiredIOPCIDevice</key>
<string>AGP</string>
<key>AELMinimumOSVersion</key>
<string>10.2.0</string>
<key>AELMinimumQuickTimeVersion</key>
<string>6.1</string>
-Hacked Section Entries: (this is what my INFO.PLIST file looks like)
<key>AELMinimumRAMSize</key>
<string>256</string>
<key>AELMinimumCPUSpeedSingle</key>
<string>350</string>
<key>AELRequiredIOPCIDevice</key>
<string>PCI</string>
<key>AELMinimumOSVersion</key>
<string>10.3.2</string>
<key>AELMinimumQuickTimeVersion</key>
<string>6.5</string>