Log on to the server with a different valid login, and run this query:
SELECT *
FROM sys.server_principals
WHERE name = 'test_user';
You should get one row, and verify that it is as you expect. E.g., the type should be 'S', is_disabled should be 0 etc.
If all of that looks correct, run this (which is the same as what you verified using the user interface)
SELECT SERVERPROPERTY('IsIntegratedSecurityOnly')
This should return 0.
If all of that checks out then we have to think of some other clever explanation for why test_user cannot login.