Alex,
I apologize for that as the information in the article changed after I responded to this issue. Error 1669 can be similar to error 1. Try the troubleshooting steps for error one as outlined below.
Try to restore your iOS device two more times while connected with a cable, computer, and network you know are good. Also, confirm your security software and settings are allowing communication between your device and update servers. If you still see the alert when you update or restore, contact Apple support.
Common errors: 1, 10-47, 1002, 1011, 1012, 1014, 1000-1020.
If these steps do not resolve the issue, see the section labeled issue not resolved in the article below.
iPhone: Hardware troubleshooting
http://support.apple.com/kb/ts2802
-Jason H.