A faulty DNS record should only have impact on name resolution, not pure IP communication and would not have any interference with a router.
One bad zone file can prevent the entire DNS server from running, at least with Bind I've experienced this. So I could see you having issues with name resolution if this is your primary DNS server your workstation is using.
If you are not able to reach the system directly by IP, then something else is going on.
You mentioned a router involved, are you trying to reach this system from a different network so you are traversing a router or are you in the same subnet?
If you are in a different network, are you able to reach other systems in the same network as the server you can't reach?
If you can, get remote access to one of those systems and try to reach the server from the machine in the same network as it, that way taking routing issues out of the equation.
That you can get to others but not that one does point more at it being a system issue over routing, but doesn't rule it out. Best confirmation still would be to get on or to have someone else test pinging that box from another on the same subnet.
How are you traversing to this network, VPN, public internet, point to point?
Is there anything you can test on the box besides SSH, it may just be the SSH daemon not working.
Although the DNS is in question, you could try using nslookup or dig to test DNS resolution.
If there are web or mail servers, you could telnet to 80 (web) or 25 (smtp) to see if it connects. Note: you don't need to do all the testing steps, just the telnet serverip 25 or telnet serverip 80 will be sufficient. If they are there, you will see a text response.
Also, running a trace route from your machine to the non-responding machine and to one of them that is responding could be helpful. Look at the steps they take, if they go different routes, then you may have a routing issue. Depending on your environment your traceroute command could be traceroute, tracert, tracepath.