We don't have net::SSH or net::SSH:perl installed...

The other way that ssh is often automated is via the Expect module, which you should be able to install without admin permissions, because it's pure Perl.

is there any compatibility so that I can take the script I've got working on one system to be able to SSH into the other systems and check them for the files, or will I need to have a copy of the program running on each system?

The question is a bit vague -- there are a number of ways you could tackle this and we don't have enough information to decide which is the best for your context.

My suggestion would be to copy this script to all of the relevant machines, and then write a separate wrapper script which could be placed on your "home" machine and which then ssh/telnets into each host and runs the script with the current arguments. (If they all supported SSH, this would be pretty easy, because you can pass the command name to the ssh binary: "ssh user@hostname farm_find.pl corpname".)