The project is seriously underbudgeted... but I feel your pain, this has been indeed promised as an easy upgrade. It is - if you have a clean site with core components only. The main problem here is the template itself, the Cleanlogic template by Crosstec has been written for Joomla 2.5/3.0 and PHP 5.6 - so the template also needs to be updated to something more up to date, otherwise you will get stuck to PHP 5.6 - which is unsecure.
Plus everything needs to be cleaned from hacked code/remnants of hacks.
So, it is not a newbie task. Luckily, I am not a newbie, I am working with Joomla since the project has been started, and accumulated a lot of experience. And on top of that, I am member of couple of core Joomla project teams, I have extensions published in Joomla Extensions Directory, listed in the official Joomla Resources list, and I am running my own hosting company.
For the price proposed I can migrate all your content to a clean Joomla instance (all assets, but the templating will be preserved), compatible with latest PHP, clean, and secured down to a reasonable level.
This is the cheapest package I can offer - leaving you with the easy task to pick up another free template which fits your needs, and make yourself the necessary adjustments.
There are other possible ways to solve your problem, but each will cost you more, than this. Interested to find out the other possibilities? Drop me a message, we can talk it through, free of charge, no strings attached.