To understand how single and double quotes work in Perl, maybe perlop helps you.

The problem at hand is really simple, and had you used strict, Perl would have told you about your usage of $dfull and $full.

I recommend to also print out the value you are actually checking with the -X test as follows:

my $dir= $part1;
if( -e $dir ) {
    print "-e $dir is true\n"
} else {
    print "-e $dir is false\n"
};
[download]

That way, you will see what expressions you actually check, and you'll find out that $path is empty, as $dpath contains the value you've constructed.