The widget code is meant for using the shop website in a frame at some other web address (not the shop website); therefore no modules or headers are shown when "executing" the shop in widget mode.

This widget mode is stored in a browser cookie, so either removing that browser cookie or waiting for it till it expires will change the shop view back to normal again for the browser where you executed a widget script.

If you want to use this widget code at the same website, you'd need to make a slight change to it, just remove the "&wdgt=true" parameter in the href url and the shop will not be displayed in widget mode.

eg. in your example you should use
http://MYDOMAIN/index.php?option=com_ixxocart&cart=topcart&oa=AddItem&oa_quantity=1&oa_id=4096

instead of:

http://MYDOMAIN/index.php?option=com_ixxocart&cart=topcart&oa=AddItem&oa_quantity=1&oa_id=4096&wdgt=true

Instead of this widget code, you can of course use the "add to cart plugin" to achieve the same functionality on your website.