AppleTV 3 on a LAN network (no internet) with a PPC Mac and iPhone I have had a few different things told to me on this situation. I have a wifi local area network set-up with  NO Internet connection.  I want to know if AppleTV will


work at all with a PPC Mac 
mirror my iPhone ie AirPlay 
work at all without Internet (again Mac and iPhone on wifi LAN).


I do connect to my Mac from iPhone 4S for a number of things now , and sync via USB (although I've heard that's not possible).
The iPhone and the AppleTV should work just fine together (with or without internet).   Note that some router models do not work well together with AirPlay so if you encounter transmission problems this should be the first suspect.

Regarding your Mac I believe that the latest iTunes for OS X 10.5 can do AirPlay. If you run an older version of OS X you should consider the most appropriate upgrade path.  It might give a better experience to buy a new mac instead of upgrading to OS X 10.5