I can login as a domain user; but not as a local user (admin or ordinary user). Kicks local users out after typing in username + password. Local users group is authorized to login locally. What else can I check?

Is it a valid LOCAL username and password?
You have changed the dropdown box from domain to machine name?

If your Domain Admin hasn't created a local account for you, and your Domain user account isn't in the local Admin group, then you'd have to talk with the DA....

You have (as an admin) to enable the Users group to login locally. Go to Admin Tools and open Local Security Directives (or something like that in english- I'm a spanish language admin). Select User Rights Asignation (or similar in english); on the right side of the window, right click on "Allow local session" (or...) and add user or group that you want to log locally on the server (watch out your decisions, anyway). By the way, for sec reasons you may want this one too: go a little down to "Have access to this machine from network" and take out the _group_ All (or All Users) that allow _anyone_ to have access to your services or log on it.