The third octets of your IP addresses are different, which means that unless you have some sort of bridging set-up on your network, the Ethernet shield won’t be able to send packets to the gateway because it’s on a different network.
I think you’ve used either the wrong IP address for the shield, or the IP address of your router (gateway) is incorrect.
This is also an odd IP address for a Blynk server. I don’t think it’s one of the Blynk cloud servers, so maybe it’s a local server hosted elsewhere that you’re using?
Are you able to ping 10.0.0.10 from your network?
Pete.