Ahh ok, your initial post said you upgraded from 10 -> 10.0.35 which is only a hotfix application. Moving from 10 -> 12 is a bit different. Do you konw if the upgrade was successful from 10 -> 11 and again from 11 -> 12? You can see by looking in the event log for upgrade start and finish records for both upgrades.
If the upgrade failed, then most likely there is something else causing problems. If the upgrade succeeded, again, clear your cache in your browser, even if you're using a private window. Also restart the app pool for the website. If you have any custom code or redirects in the web.config, you may want to review to see if it was properly upgraded or if the redirects are causing problems.