Other than sleep apnea, what might cause someone to feel tired all the time, like they have had zero sleep?

There are so many things that can cause sleep problems. Stress is a major cause. If all your tests, blood work etc have come back negative, it could be stress. My doctor gave me Mertazapine. It worked fine, but I was afraid of the side effects and possible dependency so I looked for alternatives. What I found was two natural sleep aids. Type in the names of these to any search engine to find out how they work. Melatonin and Valerian Root are both totally drug free and natural herbs. I take two of each about 30 min before bedtime and go to sleep within seconds of touching the pillow. One by itself may work for you or you may need to experiment to find a good combination that works best. I rest well thru the night and wake up ready to go. The only drawback is the Valerian Root. It has a very pungent smell/taste, very similar to soured milk, but it works so well that I just ignore the smell/taste. They are both available at drug and health stores, but walmart is cheapest. Sweet dreams.