iMac cursor, frozen upper left corner

Power down then...

Safe Boot, (holding Shift key down at startup), does the problem occur in Safe Mode? Could take 10 minutes or more.

Safe mode attempts to repair Disks & clears lots of caches & loads safe Drivers, & prevents loading of 3rd party extensions, so if Safe Mode works try again in regular boot.

Make sure the mouse is turned on with the slide switch on its underside. Also make sure it's charged.