Resolution
I recently had some restoration issues myself, I think that we both got the same error message (1013) but if we didnt than still try this. what i was told to do was go into my iTunes host file and delete the 2 lines that say "gs.apple.com" at the end. if you have no clue what im talking about, this is how you get to that file the easiest way- (on a mac* sorry if you have a PC)
minimize all windows so that your menu bar says "finder" up in the left hand corner next to the apple emblem, click "go" then "go to folder" then type in "/private" in the box. then click "etc" then scroll down to the file that says "hosts" in there, the last 2 lines should be "74.208.10.249 gs.apple.com" and
"#127.0.0.1 gs.apple.com" if you havent modified it. now **before** you delete these, i suggest copying them and saving them in a word doc just in case. but to fix your problem just delete those two lines and try restoring.
hope this helps
-Marcus