Hi kryptonic
You are using a joomla 3.0.3 version , you should first update to 3.5.1 and then to 3.6 from where later update to 3.9.2 ( these are correct steps ) since it is a joomla issue and it has nothing to do with the template i cannot be of more help on this matter - my suggestion is to move your php version to a lower one PHP 5.3 actually you are on 5.6 version and it is giving some issues ( you can see them enabling error reporting ) -
Lowering to a 5.3 should be possible to use the joomla update core feature , if not then it should be investigated more to find the issue -
I think you should hire a developer to have this fixed since it is not a simple thing to do in the correct way and avoid future issues with your website.
Hope it helps.
Regards