URLs aren't working after site migration
This indeed sounds like a clean URL problem.

Standard Drupal URLs use query strings like: www.example.com/?q=string/string/site
Clean URLs rewrite this to www.example.com/string/string/site which is better for SEO.

Check the browser's adress bar to see if clean URLs are working. If not and if you used them on the previous install, you need to either deactivate them in drupal or get them working again. You need to activate it in settings and use correct .htaccess with Clean URLs rewrite rule.

The reason why the home page is working is that there is no query string in www.example.com/