App Store doesn't fetch updates anymore
If I wanted to troubleshoot this - I would do the following:


Make a new admin account on the Mac and restart.
Log in to the new account (you might have to disable auto login for the old account)
Open Console.app and look over two log files


/var/log/install.log
/var/log/commerce.log

Open System Preferences (while watching the logs above) and unselect all of the App Store options. Turn off "Automatically check for updates"
Run the App Store App - click Purchases - sign in to the App Store.


At this point you should have dozens of log fie entries that may point to a network error, a certificate error, an account error or perhaps a permissions problem.

The App Store app is basically a web browser that runs some code, interacts with several servers and needs date/time/encryption certificates to be correct to function properly.

You also might consider installing a clean OS onto a USB drive to boot to it and do the tests if you have any security/firewall software you don't want to uninstall / disable on the main Mac OS.