Go to logitech's website and navigate to support/drivers/downloads and look for the exact model of your mouse. You may have to temporarily use a P/S-2 mouse which would have a green connector on it in any case, it would plug into the tower or laptop at the green connection port. The purple one would be for keyboard. If can't do, then borrow someone else's pc and download the driver to a CD or flashdrive then use it to install driver.
Install the driver using the old mouse for now, then just after you give the command to reboot, pull old mouse or the P/S-2 mouse out and plug in the USB wireless device for your wireless mouse at this time. Reboot and should fix.
Your issue is either driver related or defective mouse IR no good (infrared)
I'll point you in the right direction but can't help any further without the exact model# of your w-mouse.