Test SSH on the destination machine itself. If it doesn't work there, then it won't work remotely either.
You can check address resolver issues with 'nslookup', 'dig' and 'traceroute' and you can also check network issues with 'telnet servername 22'. Telnet doesn't support the SSH protocol, but you should get the server banner.
Trying different tools to reach the server will give you different error messages, which will help you figure out where the problem is.
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