I have read a lot of places that I need to connect it to the original computer I synced it to, but I no longer own that computer. Is there anything else I can do, other than sending it in to Apple?
iPod touch (5th generation), iOS 8
Place the iOS device in Recovery Mode and then connect to your computer and restore via iTunes. The iPod will be erased.
iOS: Forgot passcode or device disabled
If recovery mode does not work try DFU mode.
How to put iPod touch / iPhone into DFU mode « Karthik's scribblings
For how to restore:
iTunes: Restoring iOS software
To restore from backup see:
Restore your device from an iCloud or iTunes backup - Apple Support
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
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.
I am locked out of my iPod Touch.
