mouse connects to mac desktop but no pointer on screen

JamesHorvath wrote:

pointer frozen in top left corner

Try cleaning the optical sensor on the bottom of the mouse.

If that does not help, try another mouse.

FWIW most any generic wireless or USB mouse will work with your iMac for testing and/or until you can get a replacement Apple mouse.

Safe Boot from the HD, (holding Shift key down at startup), does the problem occur in Safe Mode?

Safe mode attempts to repair Disks & clears lots of caches, so if Safe Mode works try again in regular boot.

Is it USB or Bluetooth?

You’re welcome.

JamesHorvath Said:

"pointer frozen in top left corner"

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Reset the SMC and NVRAM:

Sometimes operations are performed and then the keyboard settings become manipulated, technically. So... Try resetting the SMC and NVRAM. Then reboot.