Rather than assume the problem is with PHP posting to a Perl CGI, first verify that you can run a Perl CGI directly. There could be a number of problems - the script doesn't have the correct ownership, permissions, isn't printing out headers, etc. If it were one of those issues - I would expect an error message rather than a white screen. More likely, something isn't working the way you expect and you are looking in the wrong broom closet.
Write the simplest hello world CGI you can. Verify it works directly. Replace the POST action to the hello world. Verify it works.
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Want more info? How to link
or How to display code and escape characters
are good places to start.