Well I'm not yet a qualfied doctor, but from my studies so far I would say the full workup for that would FBC (Full blood count), U&E (Urea & Electrolytes), LFT (Liver function test), KFT (Kidney Function Test), TFT (Thyroid Function test), HbA1c, CRP, ESR and monospot.
For good measure one might possibly add an ECG to rule out cardio, and maybe if neuro causes were suspected, a Lumbar Puncture and an evoked potential test, to rule something like MS.
If all of those were done and showed up nothing its unlikely (although not imposible) that the cause is physiological as one or more of those markers would likely be off if there was something seriously out of whack... which leaves us with the imponderables, as we might say a "functional disorder" - which is a polite way of saying we don't really know.
As you probably know there are things like post viral fatigue and chronic fatigue syndrome, which we know are VERY real conditions, but which embarrassingly do not yet have known aetiology.