I fixed my issue with LOGON failure for NT AUTHORITY\SYSTEM... which was an error when I scheduled a SSIS . My SQL Server Agent is using NT Authority account

I added NT AUTHORITY as a user to SQL Server 2005

Created one credential with my userid and password

used that credential to create a proxy account

added NT AUTHORITY to the "Prinicpal" window( not needed if the user is already has sysadmin)

On the Step I used this Proxy account to "Run as"

Make sure the account you are using as credential is added to the other server as administrator

Hopefully it works for you