How to jailbreak iPhone 4 with iOS 6.1.3?

I have used all of the most known jailbreaking programs out there, such as Redsn0w, Evasi0n, and Sn0wbreeze. When I use Redsn0w I either get two errors. One is the "Failed to decrypt kernel" error. And the other one is "Missing keys.plist" error, even though I'm using all the right ISPWs. Evasi0n just doesn't flat out work. And I never get past the DFU Pwner on Sn0wbreeze, even though I'm doing it right. I've tried downgrading from iTunes but I got the "Failed to restore" error. I don't know how else I can downgrade. Should I just except the fact that my iPhone 4 is unjailbreakable and undowngradable, or should I keep trying to figure out a way to downgrade or jailbreak?

I don't believe they have released a Jailbroken version of iOS for 6.1.3 that I'm aware of. Have you tried using TinyUmbrella to trick iTunes into believing that an earlier version of iOS is the newest one? ITunes won't let you restore to an earlier iOS version.

Do you have your shsh blobs save to your computer if you do use those and downgrade back to ios 6.x.x