How confident can we be that nobody will crack a 128-bit key?
This question seems to be asking us how fast will computers grow. No cryptanalytic breakthrough and no quantum computing essentially means no attack faster than brute force.

So will humanity at some point in the future with significant resources be able to brute force 128 bit key?
I would answer, maybe. 256 bit key Almost definetly not.

Obviously predicting is hard especially the future but assuming humanity will not self destruct it will continue to progress and it is not unreasonable to assume it will come close to the limits of what is possible.

The main discussion on theoretical limits of brute force is in minim energy requirements. I suspect we may be short on physicists on crypto stack exchange so I will try.

Brute forcing a key requires enumerating the keys. And that requires changing bits. Each bit change erases some information and there is a minimal amount of energy required for that. Lauder's limit 
https://en.m.wikipedia.org/wiki/Landauer%27s_principle 

For brute forcing a 128 bit at room temperature this comes out 262.7 Twh(the annual electricity consumption of Spain) that is a lot But not something humanity can't achieve.  By lowering the temperature we can improve on this. And some say we could build another type of computer which doesn't erase information and this limit won't apply to it. Though such a computer might go against the spirit of the question which excluded quantom computers.

So we don't actually have any good theoretical limits to prevent humanity from brute forcing a 128 bit key eventually. Which leads to my answer. Maybe.

For 256 bits the same energy limit would put brute forcing well outside the realm of the possible.