clicking on the first of the 3 files sends me to a 404 error page.

Try different browser or clear your browser's cache & cookies.

Same goes here with 3 browsers...

Same problem for me, only the extras work for direct download, the game files are all 404 errors

In this case, contact support - http://www.gog.com/support/contact

Already did.

Found a useful post from one of the users that has the links needed to avoid the 404 errors.
http://www.gog.com/forum/general/coming_soon_divinity_original_sin/post422

The support team is kinda useless on this one: their answer is just to install the (supposedly optional) downloader in order to get the files...

Use the links above, but we should have to meddle with URLs to get our game.

Yes, the support team is useless. They told me to use the Downloader (which, to their credit, apparently actually fixes the download but of course I can't and won't use it, I use a Linux box to download my GOG games).

Anyway, I found the solution on the Internet (also linked above), the links are broken (actually, looking at other game links, they seem fine, but for some reason D:OS requires slightly different links than other games).

Log in into the GOG site and open these links (one by one) in a separate TAB (while logged in!):
https://secure.gog.com/downlink/file/divinity_original_sin/en1installer1
https://secure.gog.com/downlink/file/divinity_original_sin/en1installer2
https://secure.gog.com/downlink/file/divinity_original_sin/en1installer3

EDITED: They have now fixed the URLs and added the DLC, so if you have activated D:OS you can download everything as usual from your game library (including Mac version). They'll also make it generally available for sale for everyone.

Both
https://secure.gog.com/downlink/divinity_original_sin/en1installer1
and
https://secure.gog.com/downlink/file/divinity_original_sin/en1installer1
produce a 404

The links above are outdated. First off manual download works fine from the game's card. Although now there is a problem with the GOG Downloader and it stops after the 2nd file, so you have to d/l the 3rd manually. :D
Secondly, they have changed the title/path to divinity_original_sin_game, so the links you tried lead to 404.

Give these a try or go to your account's page:
Part 1 (34MB)
Part 2 (4.3GB)
Part 3 (4.1GB)

That's really strange. The links are working properly for me even now, 12 hours later.
What's the address of the manual download links? They should look like this:

https://secure.gog.com/downlink/divinity_original_sin_game/en1installer1

You could try the old account refresh, just in case:

https://secure.gog.com/en/account/refresh/

Failing that I would suggest contacting support, although I bet that's not the answer you were looking for. :D

Jesus on a cracker!
https://secure.gog.com/en/account/refresh/ did help. I tried F5 before and everything (and I don't even use a WWW proxy).

Now all links in there work and stuff, even the manual.
Thank you!

Yep that trick worked for me too.
Arr and i wasted the weekend for a festival instead of .... ^^

the links work for me now for some inexplicable reason. i had a very exhausting email convo with the support, which kept giving me non-working links and telling me crap like weird ip issues with my provider and gog.com. they even offered me to upload the game to an ftp server, which they DID NOT DO. despite promising me TWICE. this is really really poor customer support, but at least they tried?