Contacting TurboTax didn't solve my problem. It just sent me to the voice menu, and they ended up sending me a link to "how to download", and back to my original problem.
But luckily I had an old laptop with a CD/DVD drive and a USB drive. So I ended up just copying my TurboTax DVD to a USB drive on that laptop, and then used the USB to install on my new laptop. So it all worked out.
