What version of NT are you using?

The OracleServiceSIDName is a service that runs on behalf of Oracle. This must be running in order to start the database instance.

You can start the database with the Service. For this you need to change a setting in the NT Registry

It's at --

HKEY_LOCAL_MACHINE\SOFTWARE\ORACLE\HOME0\ORA_SID_AUTOSTART

On your machine HOME0 could be someting else as would be the SID name

When this flag is set to TRUE the database will start with the Service.
However, in you case it will not start because the system datafile is missing.

It's erroring out when trying to open the database.

You can see this in the Alert Log at --

c:\oracle\ora81\admin\sid_name\bdump\sid_alrt.ora file

Did you try "connect sys/password as sysdba" and then startup mount ?

- Rajeev