To resolve the error: network connection failed, please check your internet connection, follow these steps:

1. Check Device Connection: Ensure that your device is connected to the network. Look for Wi-Fi signals or Ethernet connections.

2. Restart Your Device: Sometimes, all you need is a simple reboot to reset network settings.

3. Power Cycle Your Router: Unplug your router from power for about 30 seconds, then plug it back in. This can refresh your connection.

4. Check for Outages: Visit your ISP’s website (if possible) or call them to check if there are any service outages in your area.

5. Forget and Reconnect to Wi-Fi: On your device, forget the Wi-Fi network and reconnect by entering the password again.

6. Update Network Drivers: If you are using a computer, ensure that your network drivers are up to date. Go to Device Manager and check for updates.

7. Run Network Troubleshooter (Windows): Use the built-in network troubleshooter on Windows. Go to Settings > Network & Internet > Status, then select Network Troubleshooter.

8. Flush DNS Cache: Open the Command Prompt and type `ipconfig /flushdns` to clear any outdated DNS settings.

9. Check Firewall and Antivirus Settings: Sometimes, firewall settings can block your connection. Ensure that your firewall is not preventing network access.

10. Reset Network Settings: If all else fails, consider resetting your network settings. This will remove all saved networks and configurations. Be sure to have your Wi-Fi password handy.

With these steps, you can effectively troubleshoot and resolve the network connection failed error.