^ What Steenamaroo said, but I'll add a couple of things.
First, on the distance. Sound follows what's known as the "inverse square law" Don't worry about the math but it means that every time you double the distance you cut the sound you're picking up to a quarter of where it started. So, if your mic is 1 foot from the laptop now, move it to 2 feet and the laptop noise will only be a quarter what it was. Move from 2 feet to 4 feet and you'll get to an eighth and so on.
The same law works in reverse. If you're tracking with your mouth a foot from the mic, moving to six inches will make you 4 times louder, allowing you to turn down the gain an further minimise the laptop noise.
One other item to mention is the aiming and pick up pattern of the mic. Your
AT2020 is cardioid which means that directly behind it there's very little pick up. If you can arrange things so the laptop is directly behind the AT (rather than angled to one side or another) this will also cut the pick up.