Almost everything can be fixed or, at the very least, ameliorated but there are two ways of approaching behavioral problems with parrots. The most common way is to just treat/eliminate the symptom. In this case, the symptom is screaming for peanuts and the obvious solution is to not give him any and just plain ignore him until he gets tired and stops on its own (this is the extinction that Augie's Dad was talking about). The problem with this approach is that although it sounds perfectly logical to us, it doesn't work that well with parrots because a lot of them will not get tired and will not stop no matter what, and because it's difficult to determine whether the behavior is actually a learned one instead of a natural or instinctual one.
Some parrots will not stop screaming simply because it's not in their nature to do so and some of them will not stop because what they are asking for is something they really, really need.
The other approach is to identify the real source of the problem and address that. I always try to use the second approach because sometimes what seems obvious to us is not the real problem. In this case, I would approach it from the premise that just because the parrot is screaming "PEANUTS!" at the top of his voice, it does not necessarily mean that he is, in truth, asking for peanuts (parrots tend to use the words they know even if they are not exactly what they want in an attempt to communicate a need). Is it possible that he is asking for companionship instead but uses the only word he knows or the only one that has gotten him any results with his previous owners? Is it possible that he is in high breeding condition and his screams are just a way of externalizing his frustration? Is it possible that he feels lonely and insecure and he is screaming for a flock and/or other form of interaction/entertainment?
To accurately identify the problem you need to do a lot of observation and/or experimenting: does he scream constantly ALL the time from dawn to dusk or does he stop at times? If he stops, when exactly does he do it? At certain times during the day -like at noon when he naps? When he is entertained by food or a toy or only when he is eating or sleeping? Does he scream when he is out of his cage and interacting with you? When he is flying? Does he still scream for peanuts after a good breakfast and with a full crop? Have you tried giving him peanuts until he is full to see if he will stop asking then? I know that you said you refuse to feed him peanuts but giving him enough to fill his crop once as an experiment will not really harm him and it might give you just the insight you need. Same as giving him a couple a day until he feels more comfortable with you, then reducing it to just one medium size shell (the one with two peanuts inside), then to one single peanut... I am also very careful about what I feed my birds but stress is as harmful to their health as bad diet can be and taking away the food he loves and has known all his life cold turkey at the same time that he is going through the confusion and uncertainty of rehoming might not be the best idea. Same as ignoring his cries. You are an unknown element for him and you want him to bond with you so I think that making the transition as smooth and painless as possible even if his dieat is not the best for a while longer will be more beneficial in the long term.
The downside to the 'root' of the problem approach is that the problem might be unsolvable because you might not be able to provide what he needs/wants.
I have an eclectus that was given up because he screamed all day long at the top of his lungs (he also plucked and was people aggressive). He went to two homes that I know of prior coming here and never did stop screaming in the five years that these two homes had him (nobody knows how old he is but I calculate between 8 and 10). He doesn't scream non-stop any longer, he has recently stopped plucking (keeping my fingers crossed because he has stopped and started again in the past but never as long as this time) and he is no longer aggressive although not particularly friendly (but that's OK). The problem with him is that he will not live in a cage. Period. You put him in a cage and he will scream non-stop and nothing you can give him or do will make him shut up. I am fortunate that I have a birdroom so he can live cage-free but not everybody does and a bird that will not resign himself to been in a cage not even for a couple of hours during the day or even at night can be a huge problem (and here's another experiment for you: allow him to stay out of his cage completely for three days in a row and see what happens).
