I'm sorry to hear you are having issues with your Apple TV and iTunes.
Your post doesn't indicate what type of computer you are using, but the article below does address the specific error messages you mentioned. There is more detailed information in the links below, but I've quoted some of the highlights below:
This error typically occur when security software interferes with the restore and update process. FollowTroubleshooting security software issues to resolve this issue. In rare cases, this error may be a hardware issue. If the errors persist on another computer, the device may need service.
Security software manufactured by companies other than Apple ("third party") can prevent iTunes and other Apple applications from communicating with Apple servers or resources on your computer. Symptoms may include:
- Unable to launch iTunes
- iOS device, iPod, or Apple TV not seen in iTunes
- Unable to connect to, purchase, or download iTunes Store content
- Unable to activate, backup, update or restore iOS device or iPods using iTunes
- Unable to sync content with an iOS device, iPod, or Apple TV
- Unable to use Home Sharing with other computers, iOS devices, or Apple TV
- iTunes or computer performance issues while an iOS device is connected, syncing, or backing up
- Unable to sync with iOS devices using a Wi-Fi connection
You often can resolve these issues by updating, correctly configuring, or uninstalling security software.
1. Verify that the issue is a third-party security software issue.
There are some issues that may appear to be related to third-party security software, but may be caused by other circumstances. Before making changes to your security software:
- Verify your computer has the correct date, time, and timezone.
- Verify you are logged in as an administrative user.
- Verify the latest version of iTunes is installed.
- Verify the latest Operating System (OS) updates are installed.
- Verify your router or modem firmware is up-to-date.
- If your PC or router is using proxy settings, try connecting to the iTunes Store without using an internet proxy. See the steps in iTunes for Windows could not establish a secure connection to the iTunes Store.
- On a PC you can run the built-in diagnostics in iTunes to test your connections and generate reports. See the steps in Using Network Diagnostics to troubleshoot iTunes store connection issues.
I hope this information helps ....
Have a great day!