If for some reason in your browser the virtuemart cart (adding articles to your cart) does not work properly, in some browsers, troubleshooting can be hard. 

First check if you have an jquery problems, you can do this via the console of your browsers to see if any jquery or javascript errors occur. If this is not the case, the problem could very well be the cookie domain settings. Go to your system settings and set the cookie domains empty. to check this you can go to your php settings and see the cookie domain values. 

if this change does not work, you can delete the cookie domain lines in your configuration.php, but note that they will re-appear as soon as you update your system settings within joomla.