Edit: BLAST Steam is still lying to me.
Okay, to clarify: this only happens with Skyrim, and it happens consistently when trying to download/install it from Steam's content servers? Yet you can download/install any other game in your Steam library without an issue? Do you have a firewall/anti-virus, and have you verified that neither of those are interfering with Steam? (I can't imagine why they'd object to installing one game over another, but...who knows.) You might also want to try https://support.steampowered.com/kb_article.php?ref=1456-EUDN-2493, although again, it seems odd that your network settings would give Steam a hissy with only one game and not another.
Nuking ClientRegistry.blob usually fixes this sort of issue right off, though. Hm. You can also try deleting the AppUpdateStats.blob and see if that does it.
If you've eliminated the firewall/AV/network as possibilities and deleting AppUpdateStats.blob doesn't do it either, it sounds like it's time to send an inquiry to Steam Support. https://support.steampowered.com/newticket.php. Since support accounts are separate from Steam accounts, you'll need to create unique account details (IE: don't use the same username/password as your Steam account!).
Make sure you explain in your initial ticket that you've tried changing download regions, deleting ClientRegistry.blob, and so on. That will save you and them both some time.