It still makes no sense as to why it worked on 3 computers without a username and password but the rest didn't
Windows authorization is the default security mode in SQL Server, so the 3 computers that it worked on, the user probably had elevated privileges (or the group or domain that the user is a part of is trusted). In this mode, SQL Server will not check for a username/password, because it's relying on Windows to tell it who is OK and who is not.
In mixed mode (which you have it set to now), the users that are trusted still do not require username and password, but all other users do.