We have this very old program called WinPOPup LAN Messenger. We are moving this program to a new server with a new IP for reasons that would take too long to explain. This program requires a software installation on each computer and we have about 500 computers. The current IP, 192.168.2.3, is already configured on all computers. How can POSH help me to change this applications IP on my 500 computers? Does someone have a script that does this that I can tweak for my own environment?
That depends on how this application stores its settings. Most likely it's stored in the registry or a configuration file, both of which can be modified remotely by PowerShell. (Exactly how you do this will depend on how you've configured the target computers and firewalls; is PS Remoting enabled, can you map drives or use DCOM, etc).
I would recommend that this time, instead of configuring an IP address on each computer, set up a DNS alias instead. It'll make this sort of thing much easier in the future.