Can you be at fault for having sex with a girl that is drunk?

The potential problems are substantial.  The actual problems are unknown. Yes, you can be at fault if it proven that she was inacapable of consent.

 Speak to no one, and get a lawyer, or call me.

I don't think so.  However, in any case like this, where two people have very different versions of the "facts," credibility -- how likely it is that a person's testimony would be believed -- becomes all-important.

You were in her home and the two of you were drinking, that's not going to be disputed.  If she tells the police she can't remember what happened at night, but "feels" that she "may have been" violated, the police are likely to tell her not to drink so much next time, and go home:  that kind of testimony is so far from proving rape, much less proving it beyond a reasonable doubt, that it's a waste of time to pursue it.

If you're charged (or sued by the woman), get a lawyer.  The way you win the credibility battle is cross-examination, the lawyer's art.