80710016: Network error
If you are connecting to the network using a proxy server, try connecting with out the proxy server.
If you continue to have problems, click on the type of connection for some troubleshooting steps.
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Not very enlightening.
You say when you do the internet test everything is fine.
Please post the results of the internet connection test.
Usually when you can't sign into the PSN the test stops there.
Have you updated to the latest firmware?