Cannot Install 10.6.7 On Imac 2006 Build 9L31a

I am trying to install Snow leapard 10.6.7 on my Imac 2006 Build 9L31a & when I get to the install part it just pops up cannot be installed on this mac. I check the log and this is what comes up.

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: @(#)PROGRAM:Install PROJECT:Install-388

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: @(#)PROGRAM:Install Mac OS X PROJECT:InstallAssistant-49

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Hardware: iMac6,1 @ 2.16 GHz (x 2), 1024 MB RAM

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Running OS Build: Mac OS X 10.5.8 (9L31a)

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: PATH=/usr/bin:/bin:/usr/sbin:/sbin

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: TMPDIR=/var/folders/YL/YLp6MSdMFuOWxA5xi7toxE+++TI/-Tmp-/

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: SHELL=/bin/bash

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: HOME=/Users/DEX

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: USER=DEX

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: LOGNAME=DEX

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: DISPLAY=/tmp/launch-MvLa1I/:0

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: SSH_AUTH_SOCK=/tmp/launch-ZP3VwK/Listeners

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: Apple_PubSub_Socket_Render=/tmp/launch-v9JQlf/Render

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: __CF_USER_TEXT_ENCODING=0x1F5:0:0

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: SECURITYSESSIONID=89d0e0

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: COMMAND_MODE=unix2003

Dec 2 20:56:32 Macintosh Install Mac OS X[317]: Env: Install_Mac_OS_XVersionString=@(#)PROGRAM:Install Mac OS X PROJECT:InstallAssistant-49

Dec 2 20:56:33 Macintosh Install Mac OS X[317]: Using install media product at /Volumes/Mac OS X Install DVD/System/Installation/Packages

Dec 2 20:56:33 Macintosh Install Mac OS X[317]: Will bless Mac OS X Install DVD (disk3s3)

Dec 2 20:56:34 Macintosh Install Mac OS X[317]: Failed installation-check {\n NSLocalizedDescription = "";\n NSLocalizedFailureReason = " ";\n}

Annyone have any idea. Because lady on the phone from the apple store said it can be installed but i dont know whats going on.

Thanks.