Download the tool iFaith. It can extract and save your current 6.1.2 blobs from your iPhone 4. Also manually download iOS 6.1.2 from Apples download servers. There are websites linking to those files, such as
http://www.icj.me/ios
Then use iFaith to inject your blobs inside that iOS 6.1.2 firmware file. Then use iFaith to put your device in a so called "pwned mode". It's a temporary hack that is needed to restore.
Use iTunes 11.0.5, for later versions won't work. I think you can download it from said site, too.
You can not upgrade to iOS 6.1.3, because you don't have 6.1.3 blobs. It's too late.