Cannot remote into a server on DMZ. Ping Computer name failed.

I want to set up a new computer as our new web server. IP 192.168.2.11. Computer name is "web".
That computer now is on DMZ. On this computer, I can ping localhost, 127.0.0.1, 192.168.2.11, "www.google.com", and its own computer name "web" successfully.
There is another server on DMZ, say, IP is 192.168.2.10, and computer name is "server2". This server has been working for quite long time. This server has no problem. On this box, I can ping "web" and its IP. However, when I ping computer name, "web", it returns "reply from 192.168.2.11,.. time=52ms.." It ping takes 52ms. When I used tracert web, I got following
tracing route to web [192.168.2.11]
over a maximum of 30 hops

The problem I really have is that I need to let our web programmer put some files from internal LAN to that "web" server. Now I cannot access to that server by using windows explorer or remote desktop. On my internal computers, I can ping its IP successfully, but it fail when I ping computer name "web". I already turned off firewall and Mcfee on that server. DNS and Wins should be configured correctly. I don't have Domain. Everything is in WorkGroup. I forget to mention that server1 can access to web sharing folder by windows explorer. We have an internal DNS cache server. Do you think that DNS is the trouble maker or there is something wrong with our computer firewall?

Thanks

 

Can you RDP directly to the 192.168.2.11 IP address? If so, then it's probably a DNS issue rather than a lack of connectivity, especially since you indicated that you can ping the address. Also, is Remote Desktop listening for connections on the destination computer, 192.168.2.11? Are you able to RDP to it from the other computer which resides in the same DMZ?

 

No, I cannot RDP into that server from a computer resides in internal LAN. I telnet 3389. It failed. However, I am sure firewall and anti-virus on that server are off.
I am able to RDP to that server from the other computer which resides in the same DMZ.