Yep, i did reinstall iTunes (I don't have any other Apple software) and I keep everything (except BIOS) updated religiously. It didn't help.
To add to my previous post - when I was able to connect to iTunes that one time, iTunes started downloading 750 Mb update. About 20% into download, iPod disconnected and went into the same old spiral of death with 0xE8000068 error in iTunes. I kept it connected and tried to reconnect again, without success. I was afraid to close iTunes, so I waited until iTunes downloaded all of 750Mb, and voila - by morning, iPod was restored.. Albeit a little weird, it wasn't restored to factory settings, it just managed to boot correctly and now works. It seems to be missing some files (e.g. iTuneU won't show any subscriptions, but I can still listen and watch the lectures from iTunesU through "Music"->"iTunesU" menu).
So far so good. I'll just restore it when I listen through my 6Gb of lectures and podcasts - I'm in Hawaii on vacation now, using hotel's WiFi and I don't know how kindly the hosts will look upon 6Gb download within a day, maybe they pay per gigabyte here. Besides I ain't fixing what works.