Try going to the camera through the Finder, rather than through any application. First, kill any applications. Then attach the camera. With luck, it will show up on the desktop as a hard drive after a short pause. If not: open a new Finder window on the desktop (Apple-N) then hit the "Up" arrow in the window till you are at the level where your hard drive appears. It should be listed there. If it is, open it, and drag the items you need out of it to the desktop or a folder.

Are you connecting via USB or Firewire (iLink)? Shouldn't make any difference apart from speed - IIRC, the eMac has USB1.1, not USB2.