It depends on how your network was configured with Windows 2000 and how you ran the upgrade to Windows 2003. Chances are there's an issue with DNS/Active Directory.
A good tool to consider in the future for migrations is the swing migration or if you're just doing upgrades for hardware, you can consider using a software package from Acronis.
are we taking about client computer of server?
One cannot just install Windows Server 2003 and expect it to work automatically, one needs to take the time to learn about it and how to configure it. Try these tutorials:
http://www.visualwin.com/
http://www.learnthat.com/courses/computer/windows2003/
What edition are you using?
Are you using a workgroup or a domain in the office? You may just need to add all of the computers into the active directory.