Identify various devices on the network. Devices include all hardware devices connected to the network i.e. PC's, Servers ,Printers & Plotters nmap or maybe netdisco.
Ping remote hosts to verify the network connection. Using Perl Commands to verify network connectivity. Net::Ping, ping or Nagios.
Ping hosts along a route to isolate a hardware or software problem. Traceroute (isn't as effective in a switched environment).
See what ports various machines are using. Check to see what ports a device is using and what state these port are in i.e. Listening, Closed, Established. nmap (hint: the "-oG - " option is nice). If you are on the local host then you might want to look at NetStat.
Look up IP addresses of hosts using a device name. Given an IP address the program will be able to look up a host based on the IP address and return the host name.
host or nslookup.
Obtain information about all users logged on to a particular host (important security utility for institutions such as the college). Can see what student is /was logged onto a particular machine. Important if machine has been tampered with e.g. passwords hacked.
You probably want a log server. You could also use Net::SNMP or net-snmp I suppose.
Allow user obtain and configure time settings from remote hosts (important to allow many software packages run properly).
NTP protocol. ntpdate. IIRC DHCP can be used to update the clients time also.
Automatically send an alert (e-mail) to the college work request system detailing the detection and fault of a hardware/ software problem. Nagios (plus QuickPage if you want to send text pages-- sending an e-mail doesn't do any good if the mailserver went down or the network died).