If I had to take apart a laptop to fix a freezing problem, what should I mess with?

May be,you dso not need to take it apart.

Here are a few fixes that have helped other users resolve their ‘Windows 10 freezes randomly’ problem. You may not need to try them all; just work your way down the list until you find the one that works for you.

Update your drivers

Clear your computer’s temp files

Run a memory check

Adjust your virtual memory

Run a disk check

Run System File Checker

Disable C-States in BIOS

Read more.....

There's two things that might be wrong with it it might have a week or bad ram stick the hard drive may be worn out and when it gets warm it's sticks and then everything is going to freeze up. Here's a way to find out for free.

Don't go digging around inside your computer for one get yourself a version of Linux mint either 64-bit or 32-bit depending on what kind of processor you have install it on that computer that's freezing. And see how it runs with Linux mint on it if it stops freezing up fine now you've got a nice operating system for free if it doesn't stop freezing up I'm going to put it to you it's really not worth it for you to go buy a hard drive and RAM for an old computer when you can by a Dell m4500 from me for $325 this is a $1,500 computer it will blow whatever you've got slap out of the water why invest money in something that's 6 years old or older when for just a little bit of money you can get a truly bad boy computer call me I'm the Statesboro PC Doctor Google me

Open up the hard drive and flip the platters over. That is usually the first thing I do for my customers

run windows repair tool on it. disassembly NOT recommended -- this is likely a software problem

With no clues what "compaq" model laptop from 2011 (possibly) and what operating system, and what was running when it freezes, not able to guess accurately.