Am adding just a "kobo" suggestion, using your OP and the modification provided by ww to your script.

Anonymous Monk says:
"..D:\Prog\Perls is the location where I execute my code.."

In that case, you can get your desired result using chdir. {Updated}
Like so:

#!/usr/bin/perl
use warnings;
use strict;
use File::Spec;

my $dirname = "C:\\Users\\Me\\Desktop\\Cluster1";
my @file_to_use_later;    ## for use later
chdir $dirname;           ## add this to OP script

opendir DIR, $dirname or die "can't open directory: $!";
my @FILES = readdir(DIR);
foreach my $FILE (@FILES) {
    my $fil_path = File::Spec->rel2abs($FILE);
    print "File path:", $fil_path, $/;
    push @file_to_use_later, $fil_path if -f $fil_path;    ## check fi
+les contents later
}
closedir DIR or die "can't close directory: $!";

## test the files stored in the array variable later

for my $filename (@file_to_use_later) {
    print $filename, $/;
    open my $fh, '<', $filename or die "can't open: $!";
    while (<$fh>) {
        chomp;
        print $_, $/;
    }
    close $fh or die "can't close file:$!";
}
[download]

    $abs_path = File::Spec->rel2abs( $path ) ;
    $abs_path = File::Spec->rel2abs( $path, $base ) ;
[download]

D:\Prog\Perls\doc.txt
D:\Prog\Perls\volt.txt
D:\Prog\Perls\holiday.txt
[download]

C:\Users\Me\Desktop\Cluster1\doc.txt
C:\Users\Me\Desktop\Cluster1\volt.txt
C:\Users\Me\Desktop\Cluster1\holiday.txt
[download]