Possible to restore without using internet?

Hi,

Basically for some unknown reason any time a usb device goes off or gets removed my computer won't regonize it or any other device until I restart therefore when it comes to me wanting to restore my phone I can't use my computer and the only spare laptop I have laying around is pretty old and I can't access the internet with it. Therefore I was wondering if its possible for me to restore without using the internet or for me to restore one the laptop without the internet and then connect my phone to the computer that has internet access. If doing that will the itunes server verify the restore? Or does the verification have to be from the same computer my device was restored from?

Thanks