RUN SFC Command

1. Right-click on the Start button and click on Command Prompt Admin.

2. On Command Prompt screen. type sfc /scannow and press the Enter key.

If this does not help, try to repair system image.

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Before you do anything, right click on the taskbar and see all the things you can do in taskbar settings. Windows 10 has some different settings from windows 8. There is a lock the taskbar setting  to keep pinned apps. 

See Pin apps and folders to the desktop or taskbar (microsoft.com)

To add to what @Mary G said, if you're talking about the "Notification Area", right-click the Taskbar and select: Taskbar settings.

When that opens, scroll down to Notification area and click "Select which icons appear on the taskbar". Make sure the right ones are selected on the screen that opens, or turn on "always show" to see all of the ones you selected all the time.

Thanks for all of the suggestions. I’ve also had a running private series of suggestions from Dell support. I’ve therefore tried various things but not the system reinstall that Dell have ultimately landed on. Too much hassle. But, something does finally seem to have worked. The last couple of days at start up the pinned apps have appeared on the taskbar. Well done (assuming it stays that way) and thanks again Steve.