Are you gifted in this area or were you looking to practice on taking apart a computer and fixing it? Is anyone using the old computer? Once you clarify in your mind why you want to take it apart, then simply go to your parents and talk to them about this. If someone is still using it, you might get some push-back on this, but if everyone is using the newer one, they might be okay with this. You won't know until you talk to them.
How can I convince my parents to let me take apart my old computer? I have a new one that I share with my mom now, and the old one is really laggy and hasn't been touched in years.
Clean it up. Replace any of the "big hardware" (like fans and power supplies) and then install Linux.
Take a couple of weeks to learn a real operating system.
Enjoy being a "computer genius".
Show this to your parents... :)