For a 10 year old computer, most of the parts won’t be salvageable, so don’t worry about taking out most parts (the except will be memory if you’ve recently purchased new memory and know it’ll work with your new system).
However, do REMOVE the hard drive. Don’t wipe it. Destroy it instead. Even after wiping, information can be retrieved from it (though, admittedly, there’d have to be a good reason someone would need your information, as after securely erasing a disk, retrieval is difficult, but not impossible).
Ways to destroy it include blowing it up (fun!), dropping it repeatedly off a tall building (fun!), shooting it in the desert (fun!), or using a sledgehammer on it (fun!). Always wear safety glasses when doing so.
Once removed, donate the rest of the computer.