I have done same thing in my application.
You can add two buttons for start and stop.
When click on start, start will be disabled and stop will be enabled.
similar is the case with stop button.
Each time you start/stop the task, it will create/update a the entry in db for that task. it will update start /end time for task in DB.
At end, from DB you can find total time(sum of time spend every time on task) spend on task on the basis of start and End time.
Please find attached solution. It will demonstrate the use of Start Timer and Stop Timer functionality for each datagridview row in an windows forms application. With reference to it you can make changes as per your requirement.
Hope it helps.