The status of your On-Demand course is shown to the right of the course name.
The course below is in "Not Attempted" status:
Once you access the course, the status is "In Progress", as shown below:
To complete an On-Demand course, you must pass the course final assessment with a grade of 80% or higher. You can take the assessment multiple times. Please allow about 10 minutes for the system to update, at which point your course will be in "Completed" status as shown below: