I personally think that anyone can learn programming, given enough time, and enough effort, though obviously the amount of each required is different depending on the person.
Java and C are good places to start for practical languages. You're right, that it requires a different mindset; but once you have that, it pretty much carries across any language you'll learn. It just takes time, is all.
What you should do is set yourself some relatively easy project, and try to make it. Like, try and make tic-tac-toe in the console, using Java or C. It'll do wonders for your understanding.
If you don't know where to start; I can definitely help with that, just ask!
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