They just told me to cut the USB-plug and send it to them just for an insurance that i couldn't use the old mouse anymore, but i got the new mouse before i had to do that.
Sure, a G25 is more expensive than a mouse but you can always try
It's not necessary, they just needed some numbers from under the mouse (under the G25 in your case) and after that they just sended me a new mouse, and i didn't even bought it new, i bought it used from a friend. Logitech is great!
So give it a try and call the Logitech support and see if they can fix it. The worse thing that could happend is that they give you a NO
I have very good experiences with them. For example an optical mouse, logitech mx518 broke for me and the warranty had run out, but they still sended me a whole new mouse! that is great service!