Cannot move the arrow on the screen

If this is the mouse that came with the computer, it must be charged first as MrHoffman states.

And I am not trying to be flippant or condescending here but, as this is common cause of mouse and keyboard issues reported here, I must ask: Apple mice also have a power switch. Did you find that?

Ensure the mouse is charged.

If this is an Apple Magic Mouse, the charging cable can usually also be used to pair or re-pair the mouse with the iMac.

Try a different mouse. Wired, if you have a USB-C mouse, or with a USB-A to USB-C adapter and a USB-A mouse.

Un-pair and re-pair the mouse, and see if that clears this. To access the controls and enable mouse keys or pair or un-pair a mouse, use Control-F2 to open the Apple Menu, then arrow keys and return and escape and tab to navigate menus and controls.

You can set up a shortcut—as mentioned in the link above—to toggle mouse keys on and off.

If the mouse has failed, acquire another.

Do the keyboard keys 7, 8, and 9 move the cursor around?

If so: Control the pointer using Mouse Keys on Mac - Apple Support