If you cut the papaya it will sprout arms. If you have it inside your house if is probably why you did not get fruit. It requires polination and it has to be a hermaphrodite if you have only one and no other papaya around. Pure males have long panicles and are rare (because we cut them down), and females will produce only female flowers (with little fruit behind the flowers). Unpolinated or partially polinated female flowers will drop. Hawk moths and other insects polinate papaya and they need to make several trips.
The papaya stem is hollow. If you cut the top and put water in the core it will rot, otherwise cut it close to the ground and bury it. You do not have to dig out the roots, it will eventually rot in place.
Most people plant at least three trees, if they have room they will have more. One time I had 5 Malaysians and they were all female but my neighbor had a hermaphrodite so their tree was able to polinate mine. My mother used to come and raid my tree all the time. Female fruit is round, solo fruit has a pear shape and is usually a lot smaller. Most commercial growers will cut down the male and female trees and only keep hermaphrodites to get consistent fruit shape and quality. My philosophy is that if it is sweet, I keep it. Even if it is a female, as long as there is a tree with male flowers nearby, it is no problem.
I have fewer issues here with polination because certain trees like papaya, avocado, mango, lychee, dragon eye and most of the other tropical fruit trees are so ubiquitous in the neighborhood that I don't have to worry about polination. We just have to pick the sweet papaya when the first streak of yellow appears otherwise the birds will eat them. If the birds leave the fruit alone, the tree gets cut down, birds will only go after sweet fruit.
Happy gardening in Hawaii. Gardens are where people grow.