We know that he was a killer from an early age - he disposed of Carl Powers when they were only teenagers. He must have had a fairly decent knowledge of chemistry and science from that age then too, because otherwise he wouldn't have known how to kill him. So, he's one of those people who are naturally clever and probably excelled in Maths and Science. I'm saying Maths because of course, the more traditional Moriarty was a Maths professor. He also seems to have a good knowledge of technology. He was able to get a job in the hospital as an IT technician and has the ability to hack into nationwide screens to project his image onto - and screens in the back of taxis!
 

I agree that Moriarty for sure has comprehensive knowledge about different branch of science ( at least of chemistry, biology and technology ). I think he was very charismatic person, good leader and brilliant logistician from his childhood - I doubt he killed Carl Power all alone, he probably had some people that helped him. He also had to be very creative from the begining - it's not easy for about 12 year old child (I'm not sure how old he was) to gain botulinum toxin ( it's one of the most dangerous poison in the world, I think it's not available in common shops xD ).

I think his family was ordinary one and he was the most intelligent member. He probably despised them because they were not intellectual partners for him. Maybe his parents sometimes regretted that they had so clever (yet so arrogant) child and wished that he was average one.

What inspired him? I think that the same thing that inspired Sherlock - boredom. I can imagine that one, boring day he did something forbidden ( don't know, mabye stole something ) and wasn't punished becasue he used his intellectual advantage to avoid consequences. And that day he found out that he could do whatever he wanted to because this boring, stupid people would never be able to catch and punish him. He started to be criminal because it was more profitable than beeing a hero. Maybe at this time he changed his name to Moriarty because his original name was connection to his past and he wanted to cut it off.

And why he wanted power? Simply - because from the beginig he was arrogant and vain person and he wanted ( and still wants to ) show the world that he is the smart one and no one is clever enough to stop him.

Possibly a datk set!