so please can someone help me out here with a quick and easy way to transfer my old photos??
Use a external USB drive, that's the fasest way. Drag and drop copy one to another
Newer Mac's the Firewire is gone, needs a adapter to the Thunderbolt, or perhaps a cable you might not have on hand.
Take the folder of the G4's photo's and place it into your Finder > Computer > Macintosh HD > Users > you > Public > DropBox and that should change the permissions to you.
Or you can use the Finder >Get Info on the folder and set them to you and apply to enclosed items.
You will still need to import them into the newer iPhoto format, so don't replace iPhoto Libraries as the G4 one is likely too old to be recognized.
You can right click and "show package contents" if it's a pkg and there should be a folder called Originals you can import into the new iPhoto and thus into the new iPhoto Library.