If I were to guess as to what's happening, when cygwin tries to execute /cygdrive/c/test_error/test.pl, it notices the shebang line (#!/cygdrive/c/Perl/bin/perl.exe) and executes the following instead:

/cygdrive/c/Perl/bin/perl.exe /cygdrive/c/test_error/test.pl
[download]

Cygwin has no problem problem understanding /cygdrive/c/Perl/bin/perl.exe, but ActivePerl is not a cygwin application, so it can't open /cygdrive/c/test_error/test.pl.

The simplest solution would be to use your cygwin build of Perl when launching scripts from a cygwin application (like bash).