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On broken monitors:
I know a guy who owns a TV and computer monitor repair shop. Whenever I have a monitor fail, I take it to him and he does a free diagnosis to give me an estimate of what it will cost to fix, or if it's even worth fixing at all. If he can fix it, I might do that. If he can't fix it, or if it's not worth it, he just keeps it. He'll even take one that I just don't want anymore, working or not. Sometimes he might use it for parts, sometimes he disposes of them. It's a win-win: He gets my business and I have an outlet to get rid of my old monitors.
On the computers that are phased out, but still work, we sometimes give or sell them to employees. Sometimes, I'll have a "lunch room auction". The bidding might start at a few bucks, and not really go too high; but it's a fun way to get rid of old stuff. In the last auction I had, for example, somebody bought an old HP 720c printer (that had a tendency for the occasional paper jam) for about $10. However, the computers usually don't have the OS or any other software because we don't want to violate our software licenses agreements, so whoever gets them has to be savvy enough to take it from there. I don't want to support our "home" users.
Old hard drives, motherboards, graphics cards, etc., that still work but are no longer adequate for the office needs, I sell them on ebay, often times in large and/or mixed lots. There certainly are buyers in the market for either single 6GB, 20GB, etc. drives or lots of 5-6. This stuff usually doesn't bring a lot of money, but it goes to someone who needs it for a bargain price.
I've tried the school angle, but I've found that they don't want them because they're either too old or they don't come with the software (or both).
The other stuff, the broken motherboards, power supplies, and such, they go to the resident liberal Democrat. He spouts off about the environment and all that stuff, while I, on the other hand, love dirty air and polluted water, so he gets them. I "shame" him into taking them and disposing of them properly. What does he do with the stuff? I have no idea. He's never said, and I've never asked. (I have a sneaking suspicion, however, that he just throws the stuff in the dumpster, and is really putting up a facade.)