Microsoft says this message can indicate issues with your domain controller, and implies it could also mean issues with your network.
Your domain controller may be malfunctioning. When you log on to a
domain, the logon information is saved, but changes to your profile
may not be. If a workstation tries to join the network with a computer
name that is the same as a Windows 2000 domain name, the Windows 2000
Workstation service on all workstations participating in the domain
fails to start during system startup. Workstations already logged on
before the duplication of the domain name will continue to operate
successfully. User Action:
You can still log on, but you may want to wait until the domain
controller can be contacted. When this error is reported by
workstations in a domain, identify the computer, remove it from the
network, and configure it with a unique computer name. To identify the
computer, use STAT32, WINMSD, or another utility to resolve the name
in question to an Ethernet address. The Ethernet address can then be
used to trace the workstation.
Can you ping your domain controller for Domain A?
Can you access other network resources on Domain A, such as the internet, other servers and workstations, etc?
Try pinging the domain controller by name "serverA" and by ip address. If the name resolves to a different IP, you have a DNS issue on your network. If the name doesn't resolve at all you have a DNS issue on your network, or a network issue on your network. :)
A firewall could also block this. When you look at your network settings, is the network for Domain A listed as a "Work" network or "Public" network? It should be a "Work" network to allow the firewall to communicate properly.