|Go to Device Manager, under Mouse RIGHT click on the name of the mouse, in your case Logitech something probably, select Un-install, click OK, reboot the computer, Windows will re-install the driver.|
If that doesn't help, if you have special brand name drivers for the old o new mouse loaded in Add/Remove Programs, Un-install them, reboot, Windows will re-install the generic mouse drivers that come with Windows.
If the mouse cursor won't move while you are booting, use the Tab key to toggle selected keys, Enter and/or the Cursor keys to choose a choice, and the mouse will work once the Desktop has fully loaded.
If the mouse is USB connected, un-install the mouse driver, follow the install directions - some devices require you install driver software first, then connect the mouse, though that's usually not the case for a mouse.
A side note - I have one USB connected Logitech mouse that conflicts with some other USB connected devices - in my case it conflicts with a USB connected adapter that adapts a standard radio contolled airplane controller so that it can be used with the RealFlight program. Sometimes one or the other device doesn't load while booting, smetimes both work but the mouse does weird things. That mouse is a "combo" mouse - if I connect via a USB to PS/2 adapter that came with it it works fine connected to a PS/2 port.
You could check for a simlar problem by unplugging other USB devices.