Google spiders the content and doesn't necessarily look for links.

With or without the "www" shouldn't make any difference to the spider as long as the links point to a true destination they will still be indexed.

What script are you using for your site?

Is there a setting within it where you have specified the home domain.

A lot of the links in our front page menu do not need to be scripted with the techzonez.com domain in the urls because we have a global setting in virtua news where we can set the homepage url and this is then parsed into the pages. vBulletin works the same way.

for example:
our polls page is http://www.techzonez.com/polls.php but because we have already set the homepage,it is scripted in the menu as just polls.php. It is then parsed automatically so that the user sees the full url.