The brain is an electro-chemical system [1][2]. That is, signals propagate via potential differences created by the presence of charged ions. In the prolonged absence of oxygen, the biochemistry of the brain ceases at a cellular level. Electrical potential differences smooth-out to the level of thermal noise. Anything left radiates out as heat until the body reaches the ambient temperature of its environment.
The radiated energy still exists in the universe, but the second law of thermodynamics implies that it is unlikely to be participating in a low-entropy system like a brain again.
I have a hard time with talking of "transformation" of electrical patterns in dying brains and "Is there more to existence than we are capable of understanding?". I don't really know what these questions mean.
I've seen a couple of people die in front of me and its a deeply upsetting experience that is charged with meaning. But thats on the level of human emotional experience. On a physical level, death is just something that bodies do at some point before their constituent matter and energy goes off to do other things in the universe. Trying to unload human emotional baggage relating to human existence (principally, fear of death) onto physical processes that are pretty well understood (biochemistry) gets us nowhere, because really where do you stop?
If electrical energy is what constitutes brain activity, then what happens to that energy when death occurs?
What happens to electrical energy in a computer when we switch it off? I'd say that nothing very interesting.
"Constitutes" is also somewhat ambiguous. It's the structure of that electrical currents that depends on neural connections what I would say brain activity is.
Once the neurons are unusable, the energy by itself is just dispersed, mere electrons with no shape. So we... die.
If electrical energy is what constitutes brain activity, then what happens to that energy when death occurs?
http://en.wikipedia.org/wiki/First_law_of_thermodynamics
What is the transformation that takes place, if any?
Is there more to existence than we are capable of understanding?