Can you run the package in bids? can you do a preview from the data source component?
how are you connecting, SQL Auth or windows?
what type of connection manager is it? OLE, ADO.net, etc...
A good way to check this is to run BIDS on the server (if you're allowed to do that) and open the package. See if works that way. Not familiar with connecting to SQL 2000 but I assume an OLE connection for SQL Server would work with 2000.
If SQL authentication make sure the password is being retained in the package encrypt sensitive with password and make sure the password was entered correctly when setting up the job.
If it's windows check the account the package runs under. this may have changed with the new server and may not have access to the SQL 2000 box.
Another check is to launch SSMS from the server and manually connect to the SQL 2000 box using the same credential as the package. You can do a runas and launch mgnt studio as the account that the package runs under.
hth