iPhone 4s water damage recovery mode itunes error 2006

In what phase of the restore process does the error occur? Can you read the IMEI number? Sometimes water-damaged chips loose IMEI information, and then the phone is practically useless.

Btw. try change the battery. Sometimes the electronics in the battery is messed up because of corrosion. This would explain why it only starts up when it is connected. It might also explain the error you get: when the phone reboots doing restore, it will have to have a little bit of power available from the battery, because it, for just a short moment, can not drag power from the USB. Hope this helps. Jon