Hi computerlady143 and welcome to Seven Forums.
To make sure I understand this, you want to run a scheduled task while no one is logged on to the PC.
The PC is running and just sitting at the Logon window when the task runs.
I've never set up a task/PC to run that way...
Some other things you might consider trying:
In Task Scheduler Actions click "Enable All Tasks History".
If the task does run there should be some log/error info in the history.
Instead of logging off, just lock the PC and see if the task runs.
Depending what backup program you use, maybe it has a scheduling feature you could try.