How to diagnose a sluggish or unresponsive machine
Solution 1:
The very first thing to do (always) is to go Event Viewer and to see the recent events. Some may give you a hint of what takes so much resources. For example, it can be a Windows Update which checked for new updates, or Outlook which started to rebuild or rescan something, or Windows itself which indexed new files or whatever else. (Note: it is obviously NOT Windows indexation, since it happens only when the PC is idle).
Then you can try Resource Monitor. To run it from Task Manager, open Performance tab, then click on Resource Monitor button at the bottom. This tool will give you an overview of how CPU, disk, network and memory are used, and may help to track down "instant" processes which are difficult/impossible to see in Task Manager.
Finally, check Task Scheduler. It may give you a hint about a task which took too much resources.