Here are Apple steps: http://support.apple.com/kb/TS3694#error1611
Make sure you have a perfect USB cable. Maybe try to charge the battery before proceeding again.
If you have Warranty or AppleCare Coverage, take iPhone to Apple for resolution.
Error 1611 has been associated with the iPhones inability to hold the Restore Mode (mode where iTunes writes to iPhone) this can be due to anything. Restore Mode does need a good functioning battery to proceed. You describe some vague battery issues.
If you do not take the iPhone to Apple for help, the next step would be battery replacement.