Are you using a domain? How are the 98 systems configured to login (Windows Login or Microsoft Network Client Login)? It looks like the share you mention are on the 2000 workstations, is this correct?
If the 98 systems are not configured to log into a NT domain using domain user accounts the 98 system will try to authenticate share access on the NT/2000 systems using the userID and password used to start 98. If no matching user account/password is on the NT/2000 system then you will get the password request box.
If the shares are on the 2000 workstations they will not query the NT domain controller to authenticate access if you are using the Everyone group to assign permissions. Each workstation is its own entity and will treat authentication requests as such unless permissions specify that a domain level account has access. (e.g. Domain administrators can access NT/2000 workstations because the Domain Admins group is specifically added into the local Administrators group.)
If you are using domain accounts to log into the 98 systems then you need to specify domain level accounts or domain Global Groups as having access to local shares and files on the 2000 workstations.
Win98 has no security to speak of so shares created on 98 systems tend to give very little access problems.
Hope this helps...
