Ok, here is a version with a little "magic" done.

#!/usr/local/bin/perl -W # force taint checks, and print warnings
use strict; # install all three strictures
use File::Copy;
use File::Find;

my $path = "C:/Perl/eg"; #define full path to source folder
my $newpath = "c:/Delme"; #define  path to new folder

$| = 1; # force auto flush of output buffer
chdir($path) || die "cannot move to $path";
find (\&doCopy, $path); #Recursively search $path for files to copy

sub doCopy {
    return if ! -f $File::Find::name;

    my $subTree = substr $File::Find::name, 1 + length $path;
    my $destFile = "$newpath/$subTree";
    print "\$destFile = $destFile\n";
    #copy ($_, $destFile) or print "File $_ cannot be copied. $!\n";
}
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Prints:

$destFile = c:/Delme/example.pl
$destFile = c:/Delme/Readme.txt
$destFile = c:/Delme/aspSamples/ado1.asp
$destFile = c:/Delme/aspSamples/ado10.asp
$destFile = c:/Delme/aspSamples/ado11.asp
$destFile = c:/Delme/aspSamples/ado12.asp
$destFile = c:/Delme/aspSamples/ado13.asp
$destFile = c:/Delme/aspSamples/ado14.asp
$destFile = c:/Delme/aspSamples/ado15.asp
...
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Note that you needn't interpolate variables into strings to pass them as parameters, just pass the variable: copy ($_, $destFile) for example.