Trying for months: Issues accessing .Mac mail from desktop Mail app

Question

I have a few Macs (eMac, iMac G5, 2-iMac G3s...). User since 85.
I signed up for .Mac family pack. Gave email accounts to my family members. .Mac mail can only be retrieved from ONE (iMac G3) of the Macs. The others register that there are X number of .Mac emails in the inbox, but when one clicks on the box, the pane that should display the list of emails is blank. Every few minutes, the chime shows the same X number of emails has arrived in the inbox, starting the cycle all over again.
I have check, double and triple checked the Mail configuration for each of these Macs and see no difference. In fact, when you login to .Mac it appears to configure the Mail account automatically.
The router settings for these Macs (like port forwarding, etc.) is identical, too.
Thanks for your help
iMac G5, eMac 1Ghz SD, PMG4 500, iMac350, iMac400DV, IIci+   Mac OS X (10.3.8)  

Answer 1

From Mail Help:
"Setting up your email accounts
The first time you open Mail, it automatically sets up email accounts for you using the information from the .Mac pane of System Preferences and the Mail Setup Assistant. If no information is found, Mail guides you through the process of setting up a new account. You can create additional accounts at any time.
If you switch to Mail from another email application, you need to enter the account information from the other application in Mail. Before you begin, view the information in the other application, and write down the names of the incoming and outgoing mail servers, your account name and password, and whether it is a POP or IMAP account. If you have multiple accounts, get the information for each account.
To add an account:
Choose File > Add Account.
Choose your account type, such as POP or IMAP, from the Account Type pop-up menu and enter the information, based on your account type. If you aren't sure about some of the fields, check with your Internet service provider (ISP) or mail account provider.
General information: Enter a description of the account. The description is shown in the mailbox list. If you have multiple accounts, enter something that will help you distinguish this account from others, such as "Tom's work email." You must also specify the full name to be displayed in outgoing mail, such as Tom Clark, and the email address to use in the From field when you send messages. For a .Mac account, you must enter your .Mac user name and password.
Incoming Mail Server: Enter the server (typically a POP or IMAP server) where your email waits for you to retrieve it. For example, mail.example.com. Enter your user name and password for this mail server. If you specified an Exchange account, you must specify the Outlook Web Access Server.
Outgoing Mail Server: Enter the server (also known as an SMTP server) that sends your email to its destination. For example, smtp.example.com or relay.example.com. To see the server in use by each mail account, choose Edit Server List from the Outgoing Mail Server pop-up menu.
Further define the new account you have just created. Choose Mail > Preferences, click Accounts, and select the new account in the list.
In the Mailbox Behaviors pane, select options for storing and deleting drafts, sent mail, junk mail, and trash. The options are different for the different kinds of accounts.
In the Advanced pane, select options to enable the account, include the account when checking for new mail, to manage offline viewing, and other options.
A .Mac account is an IMAP account provided as part of Apple's .Mac services. To sign up for a .Mac account, open the .Mac pane of System Preferences and click Sign Up. You can also use a web browser to send and receive email with a .Mac account.
An Exchange account allows you to connect to your Exchange server via IMAP, and if you enter text in the Outlook Web Access Server field, Mail filters non-email related content from the server. (You can get the text you need to enter from your mail account provider.) For Exchange to work with Mail, Exchange administrators need to configure the Exchange server for IMAP access. Some system administrators may refer to an Outlook Web Access Server as an Internet Information Services (IIS) server.
For IMAP accounts, when you first connect to your mail server, all your mailboxes are automatically synchronized, so that the email messages on your computer are the same as those on the server.
To remove an account, select it in the account list and click the Delete button.
See also
setting up email"
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OR:
"About synchronizing email accounts and settings
There are two ways you can synchronize your email accounts and settings:
If you are using an IMAP account, all your messages remain on the server, so you can access them from multiple computers. Mail periodically synchronizes your IMAP mailboxes with those on the server, ensuring that mailboxes on your computer reflect actions taken while viewing mail on the server, such as marking messages as read, deleting messages, or moving messages between mailboxes. If "Keep copies of messages for offline viewing" (in the Advanced pane of the Accounts pane in Mail Preferences) is set to one of the options that stores copies of messages, Mail also downloads messages (and attachments, if that option is selected) from the server to your computer. Before using an IMAP account offline, synchronize the account so you know you're working offline with up-to-date messages.
If you have a .Mac account, you can use .Mac Sync to synchronize your account settings and your rules, signatures, and Smart Mailboxes across all of your Mac OS X x10.4 computers. To become a .Mac member, open System Preferences, click .Mac, and click the Learn More button. For more information about .Mac, visit the .Mac website at www.apple.com/dotmac/.
See also
Synchronizing an IMAP account to use offline
Synchronizing Mail accounts, rules, signatures, and Smart Mailboxes across computers
Open this for me
.Mac preferences
.Mac website"
iMac 1.9 GHz PowerPC G5 1.5 GB DDR2 SDRAM   Mac OS X (10.4.6)   Slot Loading 8X Dual Layer SuperDrive, iSight & Apple Remote; iPod Video