The PC box itself should not be hazardous waste. The monitor is.
It really is worth more as parts than as a whole. But be warned, the old CD-ROM might have an older interface that is found on the sound card. Etc.
Charities like Goodwill re-sell stuff. If it isn’t good enough to sell at a reasonable price, then they have to pay to have it hauled off. The buyers can be of any income bracket. A relatively recent item can bring in money. Do not give them junk. Think in terms of buying and selling. For PCs, there’s also issues about the “legality” of the OS and other software on it.
No charity or school I know takes PCs under 200Mhz nowadays for re-use.