Hi K.Wallace, I posted earlier about what helped for me but I don't mind reposting if it helps. Hope this gets you in the right direction
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Here's a suggestion that got all this fixed for me. It got my itunes back to connecting to the internet and allowed my iPad to go through the syncing process completely.
It also got my restore and update working from itunes on my computer. (its a Win7 64-bit by the way)
Link
https://discussions.apple.com/thread/3864037
Directions:
Close your iTunes,
Go to command Prompt -
(Win 7/Vista) - START/ALL PROGRAMS/ACCESSORIES, right mouse click "Command Prompt", choose "Run as Administrator".
(Win XP SP2 & above) - START/ALL PROGRAMS/ACCESSORIES/Command Prompt
In the "Command Prompt" screen, type in
netsh winsock reset
Hit "ENTER" key
Restart your computer.
If you do get a prompt after restart windows to remap LSP, just click NO.
Now launch your iTunes, Sync and see if it is working now.
If you are still having these type of problems after trying the winsock reset, refer to this article to identify which software in your system is inserting LSP:
iTunes 10.5 for Windows: May see performance issues and blank iTunes Store
http://support.apple.com/kb/TS4123?viewlocale=en_US