How do I get a TB of data to a new web server?

I would contact some of your local data-centers (rack-hosting, managed service providers, etc) and see about renting a vps or virtual machine for a day or two. Just be sure they allow you to bring in a disk for the initial transfer and they are aware of your bandwidth needs.

You might also just ask if they would simply help you with the upload.. They often tend to be opportunistic, inventive, and might be willing to accommodate you for the chance at getting some of your business.

You could if you have friends or employees willing to lend you a hand with their home connection, set up a torrent for the large file and set up your employees/friends as seeds. Of course you'd have to cart and copy the file to everyone. Even then, you could split the file into .rars and have "teams" send portions (taking care to make sure they don't download the files they don't have). Crowd sourcing ftw!

Find a regional ISP that's locally owned and bring a nice fat external drive that can hold all this. Walk into their office with $300 in cash, credentials for your server, and a 12-pack of beer. Pray that they have a gigabit uplink because a maxed-out 100mbit will take you over 24 hours.

That failing, look for local internet internet exchange point and find any AS that's connected to it. Make really good friends with somebody local from NANOG. Odds are you'll need to be creative. Try looking for any co-location near you.