There may be other problems but here are the ones that I saw.

In twig_client_parse, you are reading the contents of three XML files and concatenating them all into one string. That string is then sent in a POST to twig_rcvr_server.cgi where it is then passed to XML::Twig's parsefile method but parsefile expects a filename. You could use parse instead however it doesn't like concatenated files. So in twig_client_parse, you should process each file in turn. Also, in the customer and supplier subroutines of twig_rcvr_server.cgi you are trying to use $player again instead of $customer and $supplier respectively.

Here are my untested recommendations. I have cleaned up your code ever so slightly but there is still room for improvement.

# twig_client_parse
use strict;
use warnings;
use LWP::UserAgent;

my $ua = LWP::UserAgent->new;
my $server_endpoint = "http://localhost/cgi-bin/RnD/twig/twig_rcvr_ser
+ver.cgi";

# set custom HTTP Request header fields
my $xml;
my $req = HTTP::Request->new(POST => $server_endpoint);
$req->header('content-type' => 'text/xml');

my @files = glob( "*.xml" );
#print "@files\n";
for my $test ( @files )
{
    #print "this element: $test \n ";
    my $xml = do { local( @ARGV, $/ ) = $test; <> };
    $req->content( $xml );
    my $resp = $ua->request( $req );
    if ( $resp->is_success )
    {
        my $message = $resp->decoded_content;
        print "Received reply:\n $message\n";
    }
    else
    {
        print "HTTP POST error code: ", $resp->code, "\n";
        print "HTTP POST error message: ", $resp->message, "\n";
    }
}
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# twig_rcvr_server.cgi
use strict;
use warnings;
use CGI;
use DBI;
use XML::Twig;
use CGI::Carp 'fatalsToBrowser';

my $cgi = CGI->new;
print $cgi->header(-type => "text/xml", -charset => "utf-8");

my $xml = $cgi->param("POSTDATA");
print "the data $xml is received";

my $username = "abcxyz";
my $password = "xyzabc";
my $dsn = "dbi:mysql:twig:127.0.0.1";
my $dbh = DBI->connect($dsn,$username,$password) or die "Cannot connec
+t to database: $DBI::errstr";

my $sql1 = 'INSERT INTO twig_test(name,ppg,rpg,apg,g,blk)
        VALUES(?,?,?,?,?,?)';
my $sth1 = $dbh->prepare($sql1);

my $sql2 = 'INSERT INTO customer(first_name,last_name,dob,email)
        VALUES(?,?,?,?)';
my $sth2 = $dbh->prepare($sql2);

my $sql3 = 'INSERT INTO supplier(name,address,tel_no)
        VALUES(?,?,?)';
my $sth3 = $dbh->prepare($sql3);

#test
print "print successfully connected to the database" if ( $dbh );

my $twig = new XML::Twig(
    twig_handlers => {
        player      => \&player,
        customer    => \&customer,
        supplier    => \&supplier,
    }
);

$twig->parse( $xml );
#$twig->print;

sub player
{
    my ( $twig, $player ) = @_;

    my @f = (
        $player->field('name'),
        $player->field('ppg'),
        $player->field('rpg'),
        $player->field('apg'),
        $player->field('g'),
        $player->field('blk'),
    );

    print $f[0], "\n";
    print $f[1], "\n";
    print $f[2], "\n";
    print $f[3], "\n";
    print $f[4], "\n";
    print $f[5], "\n";
    #print "\n";

    $sth1->execute( @f ) or die $DBI::errstr;
}

sub customer
{
    my ( $twig, $customer ) = @_;

    my @f = (
        $customer->field('first_name'),
        $customer->field('last_name'),
        $customer->field('dob'),
        $customer->field('email'),
    );

    print $f[0], "\n";
    print $f[1], "\n";
    print $f[2], "\n";
    print $f[3], "\n";
    #print "\n";

    $sth2->execute( @f ) or die $DBI::errstr;
}


sub supplier
{
    my ( $twig, $supplier ) = @_;

    my @f = (
        $supplier->field('name'),
        $supplier->field('address'),
        $supplier->field('tel-no'),
    );

    print $f[0], "\n";
    print $f[1], "\n";
    print $f[2], "\n";
    #print "\n";

    $sth3->execute( @f ) or die $DBI::errstr;
}
[download]

Update: Replaced semicolons with commas in @f in the player and customer subroutines. Oops.