Problems transferring mail folders from eMac to Mac Mini

Question

Okay, so here’s the problem.
I just upgraded my boss - well, her computer, anyway - from an eMac running 10.2.8 to a Mini running 10.4.6. I am now having problems transferring mailboxes from the old computer to the new one. She is one of those people who have a couple of thousand messages in fifteen different mailboxes she’s created, so I really need to get them across to the new machine.
Here’s what happens when I try (both machines are ethernetted together)(if that’s a word). I open Mail (2.0.8) on the Mini, and go to ‘File’, then ‘Import Mailboxes’ (Mail on the old machine, if it matters, is 1.2.3). If I select ‘Mail for Mac OS X’, then ‘Continue’, I get the box asking for location. Select the eMac, go to ‘Users’, select the User’s folder, then ‘Library’, ‘Mail’, ‘Mailboxes’.
If I click on ‘Choose’ then, I get all of the mailboxes under ‘Items to Import’ as (for example) ‘inbox.mbox’. Click on ‘Continue’, and get a progress bar stating it is importing. It then tells me I can find them in the folder named ‘Import’ in the main Mail window. However, when I go to the ‘Import’ folder there are only three of the mailboxes, and they are all empty. No, I can’t figure out why just those three, since all of the boxes have mail in them. If I choose an individual mailbox folder I get the ‘No Valid Mail for Mac OS X files were found’ message. It will not allow me to choose the individual *.mbox files.
Okay, so if I follow the above path to the ‘Import Mailboxes’ dialog box, then select ‘Other’, and in the import box select ‘Mailboxes’ at the same location as above, I get one item to import, named ‘mbox’. Click on ‘Continue’, I get the progress bar, then the same message about the ‘Import’ folder.
But, once again, if I click on the ‘mbox’ folder under Imports it’s empty.
So I’m currently stuck. I could forward the old messages back to the same address, but frankly I consider that to be a silly enough idea that it might have been suggested by Microsoft. Does anyone have any ideas where I can go from here?
I apologize for the long windedness, but I’ve done tech support via email, and I personally always hated info-light messages like “My email keeps crashing. Why?” Please let me know if any of you need to know anything else. Thanks!
Mac Mini 1.5 Intel Core Solo   Mac OS X (10.4.6)   I am currently whistling "On the Sunny Side of the Street"

Answer 1

"There are a couple of things you seem to be missing that might or might not have a bearing on your problems."
I'm not at all surprised. I've been missing things most of my life
"First, ~/Library/Mail/Mailboxes is not the only place where mail is stored. You may want to also import the ~/Library/Mail/POP-username@mailserver account folders."
Okay, that one sounds good... unfortunately, there's no joy so far. I've tried it importing as Mac OSX Mail. If I select the [email protected] folder, I get a checkbox for each of the folders, then a brief progress bar when I click 'Continue'. There is then only one of the folders I tried to import under the 'Import' folder, and it again appears to be empty. If I try selecting any of the individual mailboxes I get the 'No Valid Mail for Mac OSX Found' message.
I get a bit further using 'Other', but not a lot. Selecting the POP folder gives me two of the mailboxes (one labeled simply 'mbox') and 'Continue' another brief progress bar... but again empty mailboxes. Selecting the individual mailboxes give the same result.
"Second, when importing as Other, Mail wants you to select the folder that contains the mbox files to be imported. Hence, when choosing that option, you may want to try importing the *.mbox folders one at a time, rather than the entire ~/Library/Mail/Mailboxes folder at once."
I was pretty certain I tried that, but I just went back and checked again to make certain. As above, I get a brief progress bar - then an empty, meaningless, nihilistic folder. Insert pseudo-intellectual 'staring into the abyss' line here.
I do have another thing I'm planning on trying. I was told I might be able to get better results if I booted the eMac into 'Firewire' mode so the Mini would just see it as a hard drive. I'll let you know if I get any results from that.
Thanks for your suggestions. Hopefully, this info will provide enough clues for you to facepalm and say "Of course! The obvious answer is..." And then fill in the ellipse, of course.
Those will work, or they won't. Either way, though, I appreciate your taking the time to think about this.