Usually with big Perl programs, they "use" libraries, that sometimes are not backwards compatible, or suddenly cease to exist after the upgrade. Or are not available for your new perl version. so check if you did not forget any library. Perl Libraries are also sometimes NOT written in pure perl, but in C (or C++) for speed (through a method called XS). So on this totally new RHEL7, you need to make sure these are there too. And copying them over is sometimes possible, sometimes not. (hopefully all your libraries are on CPAN and not in-house)

What I would do is an strace perl myperlprogram.pl and see what files are being used. There are better tools, like PrereqScanner but those need to be installed, and your machines probably do not have access to Internet, thus no access to CPAN (but if you do, it is as simple as: cpan Perl::PrereqScanner)

Also check the old version to make the new perl behave like it is an older perl (use VERSION). This is handy when your new perl does not want to run the old perl code because there is a bug, and that bug worked fine in the older perl.