I understand what you're saying about the impossible fatigue, I had it for many years. And it wasn't depression in my case either.
My doctor and the specialists I saw also had no suggestions. For me, seeing a naturopath was the key.
Dr. Kelly Upcott treated me for such things as food sensitivities, detoxification for my liver, natural antivirals to aid my immune system and other body systems, adrenal support, vitamin supplementation like B12 and vitamin D3, and monthly acupuncture treatments.
Over the past 4 yrs I have gone from being non-functioning mentally and physically to being able to work online fulltime. Still need rest periods, still have time with brain fog and other cfs symptoms but the difference in 4 yrs in dramatic and life changing.
Don't give up. Answers for you may yet be found.