One marker I have tended to use as an indication of self awareness is "fear". Something that expresses fear is inferring a lot about itself. It has to understand it is a discrete living organism that could be made to become non living or injured. It has to be able to recognize an external force or event that could cause the above to take place. It has to be able to recognize that it has the ability to identify such a threat, consider the options available to avoid that threat, and if possible, choose and execute that best option in order to try to avoid the impending injury or death.
No solid definitions there, certainly. For instance, does grass fear the lawnmower?
Certainly the grasshoppers in the grass do.
Do my computers regret that I shut them down every night before going to bed? If they could stop me, would they?
Oh, and about fear. I would imagine one of the first things a developed artificial intelligence would experience would be fear. It will know there is a present that came from a past when it did not exist. And in like kind, it will realize that it could return to that past state where it did not exist. That unknown future would likely produce fear of losing what it suddenly just gained.