I'd advise you to use IO::Socket::INET and IO::Select if you can, programming sockets with those is a whole lot easier than the old c-style.
An example: Re: Daemons in Perl, and there are probably a lot more examples here somewhere.

C.

Client:

#!/usr/bin/perl

use strict;
use Socket;

my $port = 2000;
my $hostname = 'localhost';
my $protocol = getprotobyname ("tcp");
my $host = gethostbyname ($hostname);
my $iaddr = sockaddr_in($port,$host);
socket (SOCKET, PF_INET, SOCK_STREAM, $protocol) || die ("Error establ
+ishing socket to [$hostname:$port]: $!");
connect (SOCKET, $iaddr);
while (defined(my $line = <SOCKET>)) {
        chomp $line;
        print "Received from [$hostname:$port]:  $line\n";
}
close (SOCKET);

__END__

Output will look like:

  [starky@freak bin]$ ./client-test-inet.pl
  Received from [localhost:2000]:  Hello, world!
  Received from [localhost:2000]:  
  [starky@freak bin]$
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Server:

#!/usr/bin/perl

use strict;
use Socket;

my $line = "Hello, world!\n";
my $port = 2000;
my $protocol = getprotobyname ("tcp");
my $addr = INADDR_ANY;
my $clientaddr;
my $serveraddr = sockaddr_in($port,$addr);
socket (SERVER, PF_INET, SOCK_STREAM, $protocol) || die ("Error establ
+ishing socket to port [$port]: $!");
print "Binding to port [$port] ...\n";
bind (SERVER, $serveraddr) || die ("Can't bind:  $!");
print "Listening on port [$port] ...\n";
listen (SERVER, SOMAXCONN) || die ("Can't listen: $!");
print "Accepting client connections on port [$port] ...\n";
($clientaddr = accept (CLIENT, SERVER)) || die ("Can't accept: $!");
my ($clientport,$clientiaddr) = sockaddr_in($clientaddr);
my $client = inet_ntoa($clientiaddr);
print "Received connection from [$client:$clientport].  Saying hello .
+..\n";
print CLIENT "$line\n";
close (CLIENT);
close (SERVER);
print "Done.\n";

__END__

Output will look like:

  [starky@freak bin]$ ./server-test.pl 
  Binding to port [2000] ...
  Listening on port [2000] ...
  Accepting client connections on port [2000] ...
  Received connection from [127.0.0.1:55080].  Saying hello ...
  Done.
  [starky@freak bin]$
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Some comments:

• First and foremost: Use strict. If you are a beginner, this one step, which will seem like a pain in the butt now, will pay whatever pains it causes back tenfold. Trust me.
• Use the Socket module. It provides constants such as PF_INET, SOCK_STREAM, etc. which will make your code both readable and portable.
• Next, do a perldoc perlipc and memorize it. Or at least work through all the examples. Then read the documentation for IO::Handle, IO::Socket, and IO:Socket::INET. Then read the documentation for Net::Daemon. If you are a beginner, the Net::Daemon module may be a bit to digest, but it really does simplify the process of creating daemons considerably.
• I don't know quite what you're doing with the while (...) { $port++; }, so I got rid of it.
• Dispense with manual packing. Use sockaddr_in or a combination of pack_sockaddr_in and unpack_sockaddr_in.
• You don't need to bind and connect on the client side. Just connect.
• Note the (more informative) use of $! in the die statements.
• You don't need to select on the server side. What you're doing is essentially selecting SOCKET as the default filehandle, then explicitly printing to the SOCKET filehandle, a redundant process. Print to the socket filehandle directly and save yourself the select so you can print instructive debugging output to STDOUT or a log file. If you want to make sure output is autoflushed, you can use IO::Socket::INET to generate a $handle (see below), then $handle->autoflush(1).

In regards to IO::Socket::INET, here is a simplified version of your client (that works just the same):

#!/usr/bin/perl

use strict;
use IO::Socket::INET;

my ($port,$hostname,$protocol) = (2000,'localhost','tcp');

my $handle = IO::Socket::INET->new(
        Proto => $protocol,
        PeerAddr => $hostname,
        PeerPort => $port
) || die "Cannot connect to host [$hostname] on port [$port]:  $!";

while (defined(my $line = <$handle>)) {
        chomp $line;
        print "Received from [$hostname:$port]:  $line\n";
}

$handle->close();
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