You don't say what the OS of the other server is. You don't say if the server is on the same LAN...
I am no Nagios expert, but I did set up and do maintain a Nagios Service monitoring 12 servers, as well as over 400 services on over 180 devices in three geographic locations. Monitored devices include, Windows Servers, Linux Servers, Netware Servers, SAN, Fax, Phone system, Copiers, Printers, Network Equipment and Connectivity, Uninterruptable Power Supplies and Server room Temperature and Humidity, and the list goes on. I generally know there is a problem before I get a phone call, email or someone knocks on my door.
But check out:
Linux: Nagios NRPE