re: I'm not a physisist either...
... me either, but here goes:
To eliminate gravity you'd have to eliminate mass/matter.
Degenerate matter is still matter. It does prevent heavier matter from escaping (the Pauli exclusion principle).
Most is here with sub-links: http://en.wikipedia.org/wiki/Degenerate_matter"
I don't know how (in words) it works, but (visually I've seen that) it does make sense.