Sub Categories not showin on main page

I recently moved the website to a new server and have come across another issue and am not sure where to start looking.

The website is https://www.bmnedirect.com.au. In this link http://www.bmnedirect.com.au/index.php?main_page=index&cPath=2, previously the categories would show on the page with images. Now they are not showing. When you click on the sub categories in the category menu, most of the sub cats show the products that are there, except for the following:
http://www.bmnedirect.com.au/index.php?main_page=product_info&cPath=2_81&products_id=170
http://www.bmnedirect.com.au/index.php?main_page=index&cPath=2_82
http://www.bmnedirect.com.au/index.php?main_page=index&cPath=2_84
all the other sub cats show the products.
I have gone through the database and they appear to be correct - product to category.
Show SubCategories on Main Page while navigating is set to 1
Include Product Listing Alpha Sorter Dropdown true
Include Product Listing Sub Categories Image true
Include Product Listing Top Categories Image false

Where else can I look to solve this problem as it only appears to affect the above 3. I have tried adding in a new product but this did not show either. I tried duplicating a product. The products in those categories are showing in Admin/Category and all have green buttons.

Also when you do a search for the products that are not showing - such as "acrylic", nothing comes up in the search.

After hours of trying to work out this issue I did the following:

• created a new sub category and copied a product from another sub category under the main category to the new sub cat.
• deleted the old sub category and the product in it.
  The new sub category was showing on the website - all good.
  Then refreshed the page and there they all were, back again and I didn't have to touch the other sub cats, they just appeared. Still don't know what caused this.

You appear to have Categories that hold both Categories and Products ...C

Categories are designed to hold either Categories or Products but not both ...

If you look at categories_id 14, does it contain both Categories and Products? If so, what happens if you move the Products out of categories_id 14 ...