My problem looks same.
and i have little knowledge of prestashop.
My site is earlier built by a programmer now he left for some reason. so i am building on my own by learning.
I too can't see the drop down menu of sub categories when i Hover on the main categories set in the top horizontal bar. By the way i have installed the theme "AP FOOD" for my site.
My web page is www.chennaigroceryshop.com please visit and suggest what should i do.
Many thanks
Imtiaz