Frustrated!

If you can't talk to your hoster then you need to investigate by yourself. Since use is a comile-time statement any failure in it will happen before your script even tries to run. Instead, go with require and wrap it in an eval block to trap the errors.

#!/usr/bin/perl
use strict;
use warnings;

print "Content-type: text/plain\n\n";
eval { require CGI::Carp; } or print
    "CGI::Carp not loaded: $@.\n";
eval { require Captcha::reCAPTCHA::V2; } or print
    "Captcha::reCAPTCHA::V2 not loaded: $@.\n";
print "End of script\n";
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Also, always check the full entries in the error log, not just the last line.