Q: ipod touch 2nd gen wont update

Are you sure it is a 2G iPod?

Does it have an internal speaker?

Does it have volume button on the upper left edge? If not it is a 1G.

Those can only go to iOS 2.2 with iTunes.

The last update fore the 1G i 1.3.1 that yo get here:

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)                   

https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/touchLegacyLandingPage

- A 2G to 4.2.1. Requires iTunes version 10 or higher. If a Mac it requires OSX 10.5.8 or later.