I was going to say the same thing - the files often are not really deleted although you might think they are. Most often they can be recovered.
That is really all I'd expect Princess to do - cover the cost of recovering the missing photos and files. If you approach them with that I think they might agree. Asking for big compensation is not going to go anywhere. You got the laptop back. They are not going to comp the whole cruise or offer other forms of major compensation. A lawyer won't bother with this either. It isn't worth the time and trouble. Just remember that every cruise line has a whole office floor of lawyers who are salaried and you don't.