Q: I have an iPod Touch version 2.2.1. Can I connect to WiFi?

If not this:

iOS: Wi-Fi or Bluetooth settings grayed out or dim

One user reported that placing the iPod in the freezer fixed the problem. A trick that works frequently with iPhones:

Settings > AirPlane Mode ON, Do Not Disturb ON

Power down and wait 5-10 minutes

Power up

Settings > AirPlane Mode OFF, Do Not Disturb OFF

If not successful, an appointment at the Genius Bar of an Apple store is usually in order.

Apple Retail Store - Genius Bar

Then

Does the iOS device connect to other networks?

Does the iOS device see the network?

Any error messages?

Do other devices now connect?

Did the iOS device connect before?

Try the following to rule out a software problem:                 

- Reset the iOS device. Nothing will be lost

Reset iOS device: Hold down the On/Off button and the Home button at the same time for at

least ten seconds, until the Apple logo appears.

- Power off and then back on the router

- Reset network settings: Settings>General>Reset>Reset Network Settings

- iOS: Troubleshooting Wi-Fi networks and connections

- Wi-Fi: Unable to connect to an 802.11n Wi-Fi network

- iOS: Recommended settings for Wi-Fi routers and access points

- Restore from backup. See:

iOS: How to back up

- Restore to factory settings/new iOS device.

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

Also, if you want, uptate to 3.1.3, the last update for the 1G iPod

The Settings>General>Software Update comes with iOS 5 and later.

Connect the iPod to your computer and update via iTunes

iOS: How to update your iPhone, iPad, or iPod touch

A 1G iPod can go to iOS 2.2 via iTunes and iOS 3.1.3 via

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

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