Is it permissible for a man to be at a woman's home at night if both of her parents are at home, but sleeping? What if they are awake?
They would have to be in the same room as either the man or woman. In the same house is not enough, since a closed door is effectively a different place. Since you can not see into it from outside. While sleeping only works if the person is easily roused - a deep sleeper is not an effective shomer. And in a different room is certainly not enough while sleeping, even if it may be OK if the person is awake and you expect they might enter unannounced.
A shomer is not a "game" - the person must actually guard, so anything that prevents that (loud noise, closed door, deep sleeper, etc) negates what they do.
This is on top of all the restrictions in what Menachem linked to.