Q: How do I upgrade to version 4.2.1?

Connect to iTunes on the computer you usually Sync with and “ Check for Updates “...

If an Update Appears Install it... if not... you are up to date for your particular Device...

See the Using iTunes Section Here...

How to update your iPhone, iPad, or iPod touch

Update it from iTunes on a computer as described at the bottom of this article; devices running an iOS version prior to 5.0 can't be updated straight from the device.

Click here and follow the instructions.

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Are you sure it is a 2G? A 1G can only go to 2.1.2 via iTunes. A 1G can go to 3.1.3 by

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

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

If your iPod does not have volume buttons on upper left edge it is a 1G.

Identifying iPod models

You also previously said "When I try to update with itunes it gives me an error message." What did the error message say?

Try on another computer

Then

-1 error

-1 error too

If still problem, make an appointment at the Genius Bar of an Apple store since it appears you have a hardware problem.

Apple Retail Store - Genius Bar