>So I get my hands on your laptop for a few minutes, there should be nothing you can do to impede me from doing whatever I want to it?
Correct. This is true of all my other possessions as well.
Ultimately, the physical hardware of the computer cannot tell the difference between a legitimate user and an illegitimate one. The distinction is social, not mathematical - the kind of thing one might litigate in court, rather than by multiplying some large primes together. Technologically enforcing the concept of ownership over an object implies the construction of a parallel, extra-legal system of rights management, with some final higher authority that is neither you nor in all likelihood your government. Here's how that plays out: yes, you paid for the computer, yes, you "legally" own it, but you did something to it that Microsoft doesn't approve of and so we're afraid it doesn't work anymore. Might makes right. Too bad!