Couple of notes:
(1) Why is there a wireless network icon (the one that then fails to connect)? Windows is supposed to connect to the internet via a the Mac's internet connection this is via a virtual ethernet/lan adapter.
Imagine this, imagine Parallels as a physical router and you connect your Windows machine via an ethernet cable, you don't actually run the cable physically, of course, but for Windows that's the physical equivalent, this is all done virtually.
(2) Secondly, was this VM migrated from a physical computer? Is it a bootcamp based VM? Or was it created from scratch under Parallels. If it's the first, there was something not right with the original install or check (3); the second and third, check (3).
(3) Thirdly and most importantly, I see you are running ESET, that maybe preventing the correct installation of Parallels Tools, as the KB I posted says, disable firewall and av if you are having problems (step 4 of the KB), in the video you didn't do that, also check step 3 of the KB and the corresponding kb article : http://kb.parallels.com/8865
(4) Finally, what would be important to see would be screenshots (no need for video) of the network adapters/locations in Windows, to see if the Parallels network adapter is indeed installed and enabled.
You should follow the instructions in the KB strictly and I didn't see that in the video.
The instructions in the KB are not the same as the ones you received via email (those instructions in the email are for completely uninstalling and the reinstalling Parallels Tools). Follow step by step closely, but this time uninstall ESET before installing Parallels Tools, that's all I can suggest, personally I put the blame on a conflict with ESET here, you can renable/reinstall it after installing Parallels Tools.
If you want to make another video then make it following steps 1 to 6 of the KB article.
About Teamviewer: I don't do remote assistance.
Last edited: Jan 25, 2013