Well you would have to have the phone (original) synced to your gmail account, and have updated it recently, to be able to get the contacts through the gmail account. Which can then be saved to your computer.
If you didn't have them synced from your phone to the gmail account, and/or didn't update them regularly, then there would be no way to get them unless you had access to the old phone and could turn it on. If so, then you could connect the phone to a computer via USB cord and save the contacts to the computer.