[inebriate]

you are assigning the wrong object to productid...and going by products.tpl, you want product and not productid

you have:
{include file="customer/main/buy_now.tpl" productid=$product_links[cat_num]}

change to:
{include file="customer/main/buy_now.tpl" product=$product_links[cat_num]} //(if that doesnt work, try adding .product at the end, i dont know which to use)