Q: My Son did a factory reset on his older ipod touch. Now the App Store is gone, How do I get it back?

You need to update your iPod as I said in my first reply:

You need at least iOS 2 to get the App store and use apps. If you do not have at iOS 2 (you have the original 1.1.5) then update to 3.1.3 which is as high as y can go. You get htere:

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

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

There are not that many apps still compatible with your updated iPod 3.1.3, To more easily find apps:

VintApps 3.1.3 for iPhone, iPod touch, and iPad on the iTunes App Store

apps for ios 4.2.1: Apple Support Communities

Finding iOS 4.2.1 Apps Compatible with Older Devices - Apple Club

HT4972 Touch Game 4.2.1 Apps: Apple Support Communities

apps for 4.2.1 (also works for 3.1.3)

Tip - Finding 4.2.1 apps that work on an...: Apple Support Communities

1. 4.2.1 iPod 2nd generation unable to use any...: Apple Support Communities

As I said before, you go here to get iOS 3.1.3

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

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

See if it is here:

IPSW file location for Mac and Windows

Find the Downloads on the computer.

Are you using PC or Mac?   Which version please.