Product page loads slowly

I have been working on a site that has been ported from OSCommerce by Cart2Cart service. They first did a trial port on a staging site, then on the real site. My client has all the customers and previous transactions as well as the full product entries and categories. The odd behavior that brought me to this forum occurs when single product pages are loaded. After clicking on a product, the product title, price and description load reasonably quickly. After that, there is anywhere from 8-18 seconds passage of time before the product image, the side bar, and the related products are displayed.

The staging site for some reason seems to load a little faster although with the same hesitation behavior. Disabling related products using a code snippet I found on the WooCommerce site seems to improve the load.

I will greatly appreciate if you could direct me to a solution to make the product pages load quickly. Here are the site information on both:

Staging site: https://parrot.testbed.biz
Live site: https://www.superparrots.com

They are both hosted on A2Hosting.com servers. The staging site is on a Swift account, the live site is on a better plan, Turbo account with dedicated IP number. As you will notice on the URLs, the live site has an SSL certificate installed. Neither site has any payment gateway activated as we are in the process of cleaning out the products. There are about 4500 customers, 450 active products, 350 draft products, 190 deleted products.

I tried installing W3 Total Cache which significantly slowed down the load times, say a factor of 2.

Thanks,

Cemal