This hard drive is presently in one of the laptops ? You'd need to be able to boot an operating system from something. Either an external drive, or maybe a pen drive, or a CD / DVD. Not clear what the router has to do with it.
You need to find out why the hard drive is running slow. It's probably full of rubbish you don't use. You also may have numerous programmes running in the background that you don't need to run.