When I double-click the MSSQL service on the server (Windows 2000) I go to the tab called Logon and there I see the account information is the same as what I log onto the network with (not the local administrator.) I am running the SQL Server using SQL security instead of NT authentication, but maybe that doesn't matter. I thought that maybe some sort of trust relationship might not have been set up between the computers, but that too doesn't seem to fit. I have solved the problem by doing what you said and backing up the database locally and then scheduling through Windows 2000 schedular a backup of the backup to the network (and that does work.)

Thanks for the advice. Your advice is always extremely appreciated.