Help with importing mail

I just got my Macbook Pro and migrated everything using firewire from my old iBook. Most mail got transferred except for mail from this one e-mail account. I can't even tell if all of the mail got transferred (there are thousands of them) but all of them say "The message from xxx <name@xxx.com> concerning “XYZ” has not been downloaded from the server. You need to take this account online in order to download it." Most of these mail are several years old. I only have problem with this one account; other accounts with mail equally old don't seem to have this problem. Can anyone help? Thanks!