When I used to have computers with desktop and tower CPUs, I tried to sell either the computer or its parts, but never succeeded despite they were no so outdated by then. Today selling old computers or old computers part might be harder but not impossible because as time went by, there might be people with old computers that will not longer find those parts elsewhere than directly from sellers.
I have never thought of doing this. I know that some people keep the old parts of computers to repair their currently working computers. I just find that it would be incredibly clutter to be looking at in my garage even.
Not only did I sell old computer parts for profit, but also had an entire business leaned toward this specifical thing. Me and a friend of mine would gather old PC components either from trash, or buy them for a bargain price from their initial customers, then sell them at double the price in our own store. It worked out well the time it was alive. Then some impediments occured when I argued with my friend about some things and the business fell... but it had so much potential!
I've sold several old computers via eBay. It's kind of hit or miss, because in some cases, the particular brand and model of computer or laptop you are trying to sell may have been a really popular model, and as a result there will be a bunch of other people on eBay selling the same thing. So you end up getting into pricing wars, trying to make your listing look more appealing to the consumers. When this happens, I was lucky to get even $80 or so for an old computer. You *could* break apart the computer and try to sell the parts separately, but then you're dealing with multiple shipping costs and multiple eBay listing fees, so that may not be worth it either. Ideally I usually just sell them off to someone in person, and let them know the computer is "as is". Other than that, in some cases I've taken the hard drive out and installed it on my new computer as a secondary hard drive, which was nice because it gave me more space without having a second external drive sitting on my desk.