Here is a link to the rules:
Also, the prize has just been increased to $250,000 from the original $20,000.
I don't know if ground effect would be significant with the slow-moving rotors of a human-powered helicopter. I've seen experiment results that show the effect dropping off quickly as the rotors move away from the ground (< 3m).
Stability and control will be major issues, and I believe electronics are not allowed by the rules.
And the problem is not impossible. We have better engineering tools than at any time in the past. We just have to take advantage of them.