Cygwin attempts to make Unix paths appear on Windows, which means that programs written with a Unix system in mind will work, but anything using a Windows path will not work. The likely fix for your program is not to think of Windows and to think you are on Unix:

#!/bin/perl
print "Hello World\n";
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or maybe

#!/usr/bin/perl
print "Hello World\n";
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... or alternatively, use the Cygwin syntax to get at Windows files:

#!/cygdrive/c/Cygwin/bin/perl
print "Hello World\n";
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If you don't need the rest of the Cygwin utilities or libraries and just want to have Perl on Windows, I recommend using Strawberry Perl, which gives you Perl, a C compiler and the environment to install modules.