The user should give you a clue here - Anonymous login failed. So, there is no point checking your username/passwords; they are not being used. One server is trying to authenticate to the other user an anonymous login; in other words, it is not presenting any logon credentials.

You need to check your set up. Under what user should the logon process be running? Is it a service account or a specific user?

I would guess that a "Local System" or "Network Service" account is being used; these accounts are only recognised on the local system. Although in some cases the Network Service can appear as ServerName$.

Andy