I was thinking... If you want to go the non-intrusive way and more or less communicate to the user that you're a human too (ie, not a big corporate monster) you could try to set up a system that can detect if the copy is pirated or not, after that just nag the user:
"We worked hard to bring you this game. W would really like to keep working on new games for all of you, so we insist, please buy the game! It helps us to keep the ship from sinking, and it helps you to get more awesome games made by us!"
Or something along those lines, kinda passive-agressive but "humane" enough that the user will feel it
The thing still lets the user play it, like a full game. If its just a message like that (say, in the background of the main menu or something) I doubt any hacker would "waste" their time into removing it and releasing a cracked version that the only noteworthy feature it would have is the lack of the message.
There is no big copy protection, no impenetrable wall to break down, without any challenge. Just a message. That'd steer off the big amount of hackers who are in for that kind of thrill of hacking the new thing.
EDIT: The point is, empathy is a powerful thing. The thing that allows anyone (without a mental disorder that is) to "steal" any software is the lack of connection to it. Pirates are totally detached from what they're really doing. Try to reach them not as filthy pirates, not as potential consumers, but just as plain people. That's what gets people going, that's what gets some gamers to say "I'll buy this to support the industry!", I've seen those kind of comments and I believe its a natural reaction to gaining a bit of empathy.
Also, peer pressure is also a powerful thing. Get enough people into the "I will support this!" bandwagon and soon many more will follow.