How to fix Error 2001, 2006 restore issues, possibly battery?

Hello. I bought an iPhone 4 online that said that it was stuck in error 21 and would not restore. After doing much research and trying different solutions, I am now getting error 2001 and error 2006 when attempting to restore to iOS 6.1.3 with iTunes.When attempting the restore, the "connect to iTunes screen" on the iPhone goes blank flashes quickly to a blue screen, and then to the apple logo, and then back to the connect to iTunes logo and either error 2001 or 2006 appears. (same thing when i tried a custom restore) I have the latest version of iTunes, am using a macbook pro mid 2012, am using an apple usb cord, and do not have any other things connected to my laptop. There is no battery icon that appears when the iphone is connected in iTunes, and the iPhone only is on when connected to the macbook. Will replacing the battery be the solution to having a working iPhone? (there is no warranty with apple) or have i bought a phone that cannot be repaired?

also the top water sensor indicates that there was water damage