How much time does it take for the bitcoin-qt window to show up in OS X 10.4?
When you open the Mac client, it first displays the loading screen for a while :



After that it displays the main screen and starts synchronizing :



Note that the client is really slow and might take a while to load. If it's still not displaying the loading screen after a minute, try opening it again. As far as I know the Mac client doesn't have any requirements for installation.

To diagnose the issue, please perform these steps :


Go to Activity Monitor (it's in the Utilities folder) and see if Bitcoin-qt is running. It should be.
Open Console (also in Utilities) and see if there are any errors about Bitcoin-qt.
Restart your Mac. It may help.