Another alternative to the Redsn0w jailbreak for OS 3.1.3 is Sn0wbreeze as iH8sn0w have release a new version of their program to work with OS 3.1.3.
Sn0wbreeze is essentially a Windows port of the Dev Team’s PwnageTool. It allows you to create custom IPSW firmwares (allowing you to maintain your current baseband when updating).
The Sn0wybreeze jailbreak ONLY jailbreaks iPhone (iPhone 2G, 3G and 3GS (with old bootrom) so if you have an iPod Touch, you will still need to use Redsn0w.
DO NOT use custom boot logos with the iPhone 3GS as you will get an error when installing it.
There is no current jailbreak (Sn0wybreeze or Redsn0w) for the iPod Touch 3rd generation or iPhone 3GS with the new bootrom.
Click to download: Sn0wbreeze OS 3.1.3 (377)