Of course we can't diagnose your cockerel. We can suggest treatments that might effect an improvement in the condition, but that's about it.
Dizziness and an unsteady gait and balance issues are, as you've already considered, neurological. Starvation, dehydration, hypothermia and hyperthermia, and injury can all produce these symptoms. But so can avian viruses.
To effectively treat neurological symptoms, you first need to elevate glucose levels by putting a little sugar in the drinking water or syringing it into his beak. This can immediately feed the brain and quiet some symptoms. This can tell you he may not be getting enough to eat and to address that.
The other important treatment is vitamin E. It needs to be in highly concentrated form - E 400iu oil from ordinary capsules found in the vitamin aisle for humans. Pop on directly into his beak and do this once a day for several days. If there's a deficiency, this may correct it. Symptoms should disappear in just a few days.
If symptoms persist with these treatments, then you might then conclude there's a virus involved that is attacking the nerves and brain and perhaps other organs.