Why does my network go down every night?

In the meantime, I'd turn my eyes towards your Windows server for a number of reasons.

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You mentioned the server is running Windows 2003, which means that you've got Active Directory installed and this machine is acting as a primary domain controller (PDC). Due to its role, it's most likely acting as a master browser for your Windows network as well. This means that the server contains a view of the whole network, so other workstations consult it to find out what resources and machines are available. If for any reason your network's master browser goes down, these services are temporarily unavailable until a new master browser is elected.

The problems you are experiencing can be a combination of a Master Browser problem, and DNS services running on the Windows 2003 server.

My suggestion in such cases is to consult the server's event viewer and look for error messages that might give you a few clues as to where the problem is. Make sure you check all log files and use the Event ID number to consult Microsoft's support page (support.microsoft.com) as you're likely to find your solution there.