The iMac is trying to access files previously owned by the user on the eMac, but these files live on a G4 on the network? Just making sure I understand the situation.
If all of the files were previously owned by a user, let's call it user1, on the eMac, and that user doesn't exist on the iMac, then you have a couple of options.
The first is to go to the G4 and right- or ctrl-click on the folder that contains all of the user1-owned work files. Select "Get Info". Expand the "Ownership & Permissions" tab, then expand the "Details" tab. Next to "Others", select "Read & Write". Then press the "Apply to enclosed items..." button, and confirm that you want to make the change.
Note that this method bypasses the slightly subtler issue of what user and group own the files, because it makes the files available to everyone.
A second possible solution would be to change the owner of all of these files to the user that the iMac uses to authenticate on this server. This preserves the idea of ownership while making the files available to that particular user.
