Uninstall, download the 1.1 and 1.2 offline patches, disconnect your computer from the internet, reinstall, and apply the offline patches.

EDIT: Pretty sure 1.2 doesn't automatically update to 1.3. Just fresh installs. That means you can turn your internet on at the end of that, of course :)

This doesn't seem to work. After entering the reg. key with the internet connection offline, the installer simply closes. If I try to install patch 1.1 or 1.2 at this time, I'm told the game version is invalid or incomplete. If I try to start the game, it simply asks for the reg. key again, and then closes when no internet connection is online. If I turn the internet connection on, it starts auto-patching to version 1.3...

You don't need to enter your registration key. You should be able to just update.

That "invalid or incomplete" message is often the result of either mods (which I'm assuming aren't a problem because it's a fresh install), an antivirus product, or the wrong 1.1 patch. The first thing I'd check is which version of the 1.1 patch you have. Different versions have different 1.1 patches, while the 1.2 and 1.3 patches are universal.

If you're sure you have the right patch, this thread may be relevant.

There may be game files that are left over from the uninstall that are causing this, as well, though I've never heard of it happening before. Still, if it's not the wrong patch or the antivirus, I'd check for and delete any files left over from the uninstall.

You shouldn't need to be offline.

Reinstall it, let it automatically install the day 1 patch, then install manual patches 1.1 and 1.2.

Being online won't automatically install the patches, as it asks you before-hand if you want to download them.