Thanks a million for this solution!
It wasn't all that was needed though. I had to also follow the instructions here:
Before i did that, this is how it all went down:
1) downloaded the files and copied them to the directory "%userprofile%\Documents\Telltale Games\The Walking Dead\SyncFs\Data\WalkingDead104". Temp-folder was already empty.
2) started the game, clicked to continue and waited out the normal not responding -state.
3) went to download and clicked "get" and it almost instantly switched to "installed".
4) went on and clicked play for episode 4 and it started, but the graphics were buggy (missing textures etc)
5) restarted the game and even though the files were still in the 104-directory, ep4 had gone back to "get"-mode and efforts to download it just resulted in the normal "connection failed"-error instantly.
Then, as instructed in the above mentioned thread:
1) i copied the folder WalkingDead104 also to "C:\Program Files (x86)\Telltale Games\The Walking Dead\GameData\Pack" and started the game.
2) After clicking continue, the start screen where the news roll horizontally just would not go away (waited 5-10min), but the process was responsive so i just left it hanging there in the background while doing other stuff for a long time, maybe an hour or so.
When i checked if it had advanced, there was the login screen asking for my telltale credentials.
3) i logged in and went to the download-section and now everything seemed right and ep4 was in installed state.
4) started to play ep4 and everything seems to work normally now
Of course, what telltale is making us do is completely unacceptable, but it works now so thanks to all of you who help people getting the game working and good if this post helps someone else.
Telltale: You owe the customers an official apology and a reasonable compensation for this mess. E.g. a free game that works.