Edit #2: Solition to my problem was found - it has to do with Bigfoot networks Winsock and seems common:
Confirmed solution from killergaming.com works for iTunes 10.7.0.21 running on Windows 7:
"Depending on the version of Windows (I'm running 7), you can click Start -> All Programs -> Accessories, right click on Command Prompt and choose Run As Administrator.
Type 'netsh winsock reset' press enter, and then reboot."
I didn't get the "The LSP was not mapped correctly. Would you like to re-map the LSP?" message. Tried this and iTunes is working fine now.