Q: connect mac mini to imac G5

OK, on the G5...

Make a New Location, Using network locations in Mac OS X ...

http://support.apple.com/kb/HT2712

10.5, 10.6, 10.7 & 10.8…

System Preferences>Network, top of window>Locations>Edit Locations, little plus icon, give it a name.

Setup Screen Sharing & such again.

10.5.x/10.6.x/10.7.x/10.8.x instructions...

System Preferences>Network, click on the little gear at the bottom next to the + & - icons, (unlock lock first if locked), choose Set Service Order.

The interface that connects to the Internet should be dragged to the top of the list.

If using Wifi/Airport...

Instead of joining your Network from the list, click the WiFi icon at the top, and click join other network. Fill in everything as needed.

On the G5>Sys Prefs>Security>Firewall tab, what does it show there?

Great news, thanks, sorry it took so long!