Just to be clear on the setup: you have a computer that has a DVD drive, but no Internet. That's the computer you want to play on. You have two other computers with Internet and no DVD drive.
I haven't tried this, but theoretically you could install Demigod on your machine. Use the "archive" option to make a copy of the install. Copy the archive over a USB key to one of the computers with Internet. Install Impulse, login as you, and unpack the archive (effectively installing Demigod).
Patch, then repeat the archive process in the other direction.
That is obviously a PITA, but I think it'd work. I really don't understand why your computer can't get on the Internet though, you can't just move it temporarily to replace one of the other computers and use its connection?