The passwords you have set up are for the user accounts.
It's the User accounts that have passwords, not the machines.
( This may seem a trivial distinction, but it's important later. )

By default, XP in a workgroup does not use these user accounts for network
access.   It uses something called Simple File Sharing, which uses the open
Guest account.

You need to disable Simple File Sharing, and then assign users
the necessary permissions on the shared folders.

Here's an example of setting up shares with user permissions:
http://www.practicallynetworked.com/sharing/xp_filesharing/

By default, a Windows XP computer in a workgroup allows networked
access by all users on all computers.

You can create a network password for the Guest account.  Anyone who
wants to access the computer over the network will be prompted for
that password:

1. Click Start | Run.
2. Type "control userpasswords2" in the box and click OK:
3. Click Guest.
4. Click Reset Password.
5. Enter a new password, confirm it, and click OK.

If the computer runs Windows XP Professional, there's a more powerful
access control method available, based on user accounts.  Ron Lowe and
I have written a web page with full details:

Windows XP Professional File Sharing
http://www.practicallynetworked.com/sharing/xp_filesharing/index.htm