Accessing Domino iSeries at two addresses for iNotes

We have an iSeries hosting Domino for two distinct private networks that 
are using different IP schemes, thus it has a different IP address bound 
to each NIC port.  The Domino server responds fine to anyone using a Notes 
client on either network and responds find to anyone using iNotes from the 
original network.  However, anyone trying to access the server from the 
second network (just recently set up) fails with a "Web Page cannot be 
displayed" almost immediately.  The speed of the response makes me think 
that it is finding the server and being rejected for security reasons (as 
opposed to not finding the server at all or finding the server but timing 
out due to the server being busy).

Any suggestions for how to get the server to respond to either network?

I did notice that the IP address for the new port is not present on the 
hosts table, but it is using the same name for both IP addresses, so I am 
concerned about putting the same server name into the hosts file twice. Is 
this a problem?

Thanks in advance,
Patrick