It sounds like you're primarily having difficulty with your Apple TV on a wireless network. The following article covers that issue in depth:
The whole article is useful and I would give it all a read-through, but I pasted the "Network troubleshooting" section below for quick reference:
If you're not able to associate with a wireless network:
- Check the IP address Apple TV is using. If it starts with 169.x.x.x, then the router or base station may not be configured properly. Check to see if DHCP access is available or configure Apple TV with a manual IP address.
- If DHCP is available, go to Settings menu, select General then Network and Configure TCP/IP. Make sure the Apple TV is set to Automatic.
- Check for any obstructions and adjust the location of the base station and/or Apple TV if necessary.
- If security is enabled on the network, temporarily disable it on the base station and try connecting again.
You can also check the following articles to see if any apply to your network:
- Apple TV: Troubleshooting wireless connections
- Configuring Firewalls on Windows for use with Apple TV
- Apple TV (1st generation): Wireless networking list does not display my wireless access point's name
- Apple TV: WPA-Enterprise encryption does not ask for a user name
- Apple TV: Switching between wired and wireless networks
- Apple TV: Connections through proxy servers are not supported
Hope that helps,