Q: Hello, Does it cost money to get your iPod touch reset?

It is free but you should make an appointment at the Genius Bar of an Apple store.

  Apple Retail Store - Genius Bar

https://www.apple.com/retail/geniusbar/   

Did you try this:

Place the iOS device in Recovery Mode

https://support.apple.com/en-us/HT201263

and then connect to your computer and restore via iTunes. The iPod will be erased.

If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled

https://support.apple.com/en-us/HT204306

If recovery mode does not work try DFU mode.

How to put iPod touch / iPhone into DFU mode « Karthik's scribblings

https://geekindisguise.wordpress.com/2009/07/16/how-to-put-ipod-touch-iphone-int o-dfu-mode/

For how to restore:

Use iTunes to restore your iPhone, iPad, or iPod to factory settings

https://support.apple.com/en-us/HT201252

To restore from backup see:

Restore your device from an iCloud or iTunes backup - Apple Support

https://support.apple.com/en-us/HT204184

If you restore from iCloud backup the apps will be automatically downloaded. If you restore from iTunes backup the apps and music have to be in the iTunes library since synced media like apps and music are not included in the backup of the iOS device that iTunes makes.

You can redownload most iTunes purchases by:

Downloading past purchases from the App Store, iBookstore, and iTunes Store        

https://support.apple.com/en-us/HT201272

If problem what happens or does not happen and when in the instructions? When you successfully get the iPod in recovery mode and connect to computer iTunes should say it found an iPod in recovery mode.

or

If you previously turned on FIndMyiPod on the iPod in Settings>iCloud and wifi is on and connected go to iCloud: Find My iPhone,

sign in and go to FIndMyiPhone

https://support.apple.com/kb/PH2696?locale=en_US&viewlocale=en_US

and use Remote Wipe

https://support.apple.com/kb/PH2701?locale=en_US

to erase the contents of your device. If you have been using iCloud to back up,

https://support.apple.com/kb/PH12519?locale=en_US&viewlocale=en_US

you may be able to restore the most recent backup to reset the passcode after the device has been erased.

You can also wipe the iOS device by installing the FindMyiPhone app on another iOS device and using that app to wipe the device.

The restore process itself is free, but if your Internet provider has a monthly data cap, you may be faced with a $20 bill if you go over (the software update file is about 2GB in size).