However, I have been woken up with a sex act that was started while I was a conscious and unable to give consent before the act was started.... I don't consider that rape.
That's fine, but other people might and you don't get to confer your consent onto them.
When I am in an ongoing relationship, there is implied consent... I think this is true in most adult relationships (when was the last time your lover ever asked you before initiating sexual activity).
My partner has told me she is absolutely fine with being woken up that way so that's obviously not rape, if there is consent there is consent. I wouldn't however presume that all sexual partners feel the same way.
But this PSA is not directed at married people, it's directed at young men whose judgment on implied consent is often not very sound. Let's say a woman has sex with a guy, did not enjoy it and mentally decides not to do it again and they go to sleep. Then the guy tries again while she is sleeping. This is a case where the consent is not given and is not appropriate.
I can get that calling this "rape" is problematic because rape covers such wide range of things that this seems to make light of, but there should be no difficulty in understanding that consent may be withdrawn and that a sleeping person is unable to communicate that.
This seems complicated.... many people have sex while both choosing to use drugs or alcohol. If this is an activity that two adults choose to engage in, how do you decide where the line is?
It's not easy and there's no clear line that can be established that will work for all situations.
Being slightly inebriated is not an impediment to giving informed consent but if someone is so drunk that they don't know where they are this is obviously not someone capable of giving consent.
Like many things you'll have to use common sense and judgement to draw the line and like many such things these lines are blurry.