Did you also check if the attached schedule is enabled? When the job is enabled, but don't display a "next run" in the Job Activity monitor, most of the times the schedule isn't enabled. This will happen if the end-date of the schedule has been passed or if the schedule was set to a one-time occurrence.
Open the properties of the job and navigate to the attached schedules window. Check the box "enabled" in the Job schedule properties.

And of course: if the SQL Agent service is not started, no SQL jobs will be executed (as you mention in your last post).