This is a Windows 2003 (or later) machine that gets switched on every morning, but no one logs on until some hours later.
I want to use the time in between to run a back
There is, if you're using Active Directory. If you can isolate the computer to its own OU or use WMI filtering, you could assign a GPO which has a startup script for the computer. This would ensure that even if someone went in via safe mode and disabled the Task Scheduler, upon startup and connection to the domain, the script would run.