This is much easier with the Net::Frame library. It works fine on Windows / Strawberry (which I gather you're running based on the shebang in your code).

<shameless plug>You can also check out the Perl Packet Crafter (PPC) which provides a scapy (http://www.secdev.org/projects/scapy/)-like interface to the Net::Frame suite.</shameless plug>

POD: http://www.vinsworld.com/software/ppc.html
Direct Download: http://www.vinsworld.com/software/ppc.zip

In your case, your TCP SYN packet is as easy as:

VinsWorldcom@C:\Users\VinsWorldcom\tmp\ppc> ppc -i "Wireless Network C
+onnection"
Welcome to Perl Packet Crafter (PPC)
Version:  1.02
Copyright (C) VinsWorldcom 2012

Wireless Network Connection

ppc> $r = srp( packet( ETHER, IPv4(dst=>'www.google.com',id=>'19245',f
+lags=>NF_IPv4_DONT_FRAGMENT),TCP(dst=>80,seq=>'13456')) );
Sent => Received


ppc> $r->report;
Packet 1
  Sent: Sat Mar 14 20:03:17 2015 (1426377797.565053)
ETH: dst:xx:xx:xx:xx:xx:xx  src:xx:xx:xx:xx:xx:xy  type:0x0800
IPv4: version:4  hlen:5  tos:0x00  length:40  id:19245
IPv4: flags:0x02  offset:0  ttl:128  protocol:0x06  checksum:0x3092
IPv4: src:192.168.10.105  dst:216.58.219.196
TCP: src:5443  dst:80  seq:0x3490  ack:0x0000
TCP: off:0x05  x2:0x0  flags:0x02  win:65535  checksum:0xe6ae  urp:0x0
+0
  Recv: Sat Mar 14 20:03:17 2015 (1426377797.591432)
ETH: dst:c0:cb:38:08:46:76  src:58:6d:8f:78:ad:40  type:0x0800
IPv4: version:4  hlen:5  tos:0x20  length:44  id:39786
IPv4: flags:0x00  offset:0  ttl:55  protocol:0x06  checksum:0x6931
IPv4: src:216.58.219.196  dst:192.168.10.105
TCP: src:80  dst:5443  seq:0x15f689c0  ack:0x3491
TCP: off:0x06  x2:0x0  flags:0x12  win:42900  checksum:0x87b4  urp:0x0
+0
TCP: optionsLength:4  options:02040596
  Interval = 0.026379 secs


ppc>
[download]

Note the MAC's above have been obscured. And you can specify your source IP and TCP port if you want, although I didn't. Note if you "spoof" your source IP, you won't get the response packet - that should be pretty obvious.