> computers cannot think

You forgot to add the most important word to that sentence - *yet*.

There are plenty of things computers can't do yet. I wouldn't rule out thinking just yet. Remember we are still in the early stages of computing. Once silicon is replaced with biological chips, then all bets are off....

What even is thinking, consciousness and sentience? The philosophers can't give us a good answer to that one but there is a range of possibilities. That's why I think arguments around thinking and sentience are misguided. A machine doesn't need to be conscious to beat you at chess.
I don't think it's correct to apply Godel to AI in the real world. Godel's incompleteness theorems are basically:
1. For any consistent formal system, there will always be statements that are true, but are unprovable within the system. 
2. Therefore, the system cannot demonstrate its own consistency.

Godel only applies only to formal systems. Back out in the real world, axioms don't need proving. If it works, it works. Birds fly yet they don't know how. And, the axioms will work if they are at least an approximate description of reality.
If you're interested then we could talk about how badly Turing tends to get misapplied AI discussions.