No unfortunately it only runs on G3 Macs
Mac OS X 10.6 (Snow Leopard) will not work on a Mac with a G4 processor as it requires an Intel processor based Mac. A G4 (867 MHz and faster) can run Mac OS X 10.5 (Leopard).
The iMac G4 is able to run any version of Mac OS X up to and including, version 10.5 (Leopard).
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Mac OS X 10.4 "Tiger" will run on a PowerPC G4/800MHz machine. It is the latest OS that Apple will support on that processor, however. At this writing (January 2010), Mac OS X 10.4.11 is the latest version of Tiger.
The PowerBook G4 was introduced in January 2001 and would have originally had Mac OS 9 installed. The first version (10.0) of Mac OS X, known as Cheetah, was introduced in March 2001.
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If it has an Intel or G5 processor, then yes. If it has a G3 processor, then no. If it has a G4 processor, then it depends on the processor speed.
The run Skype on a G4 you will need to have Mac OS X v10.3.9 (Panther) or later (See links below).
Mac OS X 10.3.9 is nearly five years old (which is a long time in computer operating system years) the current version of Mac OS X is 10.5.7. The minimum requirement for the latest version of the Safari browser is 10.4.11. To update your browser you will need to update your version of Mac OS X. Mac OS X 10.5 (Leopard) will work on an iBook G4.
The eMacs were discontinued in 2006. The earlier versions with a G4 processor running at less than 1GHz can run Mac OS X 10.4 (Tiger). The later versions with a G4 Processor running faster than 1GHz can run Mac OS X 10.5 (Leopard). Select About this Mac from the Apple menu (top left) to determine the speed of the processor.
iTunes 9.2 will work with a G4 processor but it does require Mac OS X version 10.4.11 or later.
No because the Mac App Store requires Mac OS X 10.6.6 which is not supported on the old G3/G4 iBooks.