Could I/someone set up a martial arts competition like the very 1st UFC or is it illegal now?

With enough money nothing is illegal. That said it would still look more like MMA. The groin strikes didn't change the dynamics of the first UFCs too much, and the better overall fighter(puncher, kicker, grappler) is going to win. Sorry, you can't convince me a bad fighter is going to beat a good one just by kicking him in the nuts. Especially when they're under the effects of adrenaline, and their pain tolerance is through the roof. Also bear in mind the other guy can kick you in the nuts too, its not really that complicated a technique. You do not want a Thai Boxer to kick your family jewels.