Cannot Login without using the @database_name

@database_name

I have checked TNSPING, listener and SQL.net and all checkout AOK. The problem follows

c:\set ORACLE_SID=database_name

c:>sqlplus /nolog

SQLPLUS> connect sys as sysdba

enter password:

ORA-12560: TNS: Protocol adapter error

-------------------------------------------------------------------------------------------

I CAN ONLY CONNECT USING THE @database_name

SQLPLUS> connect sys@database_name as sysdba

enter password:

Connected

Any Ideas would be greatly appreciated.  I have been given this Oracle database after another DBA left.  The only differences from this database and the other oracle Instance follows

a) The %PATH%   has both the dbhome_1     and  client_1    in the path and it's installed as follows