Whats the best method to clean inside an old laptop?

Never vacuum electronics. It creates static electricity.

Those stains resemble cig tar or pot tar. You will need an electronics cleaner.

DustOFF is pretty safe to remove loose dust.

Just don't shake it or spray liquid.

Oh, avoid using electronics in or near a kitchen. Grease in the air can cause you problems.

go to an electronics store and get 2 cans of electrical cleaner is the best way and till the case so it runs out , cost you $25 but it will be  clean , CRCsell it under electrical cleaner .

First, use a wrist strap. Electrostatic discharge can damage electronics. The voltage needed to fry an electronics chip is a lot less than you can feel. And it's easy to create. Moving while wearing clothes can generate it.

The best way to clean the interior is to start by vacuuming the interior. But, it can't be any vacuum. It has to be one specially made for use on sensitive electronics. The "497AJM" is such a vacuum. Do a web search for it. If you use a vacuum not specially made for electronics, you risk causing damage from electrostatic discharge.

Next, use compressed air to blow out remaining dust. 

Chances are you don't have a 497AJM or an air compressor, and you are not going to get either. 

If you don't have an electronics vacuum or an air compressor, buy some cans of dusting spray, and use that. Observe precautions on the label.

You can also use a soft brush. But, it should be "ESD Safe." If you use a cloth, it should be an anti-static or non-static cloth. 

And don't worry about the stain. You could cause more damage by trying to remove it. 

Good luck with that but you might want to wear an anti-static strap BEFORE touching anything inside an you might want to get an anti-static cloth as well...

N.Shadows 

Go to the auto parts store and purchase a can of mass flow air sensor cleaner it'll cost you $12. 

Take your laptop outside take the battery out hold your laptop on its side and tilt it backwards so all the liquid that you spray is going to come straight out of the laptop.

Then spray away all of the dirt out of the fan and out of the cooling fins and any place else that it happens to be lurking.

And then dry it up with warm air not hot air from a hair dryer.

Why you have the back off if you can regrease the CPU heatsink you might as well do that in the process.

If you can't find some heat sink grease go to the auto parts store and on the counter for a dollar is spark plug anti-seize it's actually better to dissipate heat then expensive heat sink Grease.

a can of air duster.

Usually blowing the dust off with 'canned air' (or a compressor) will be enough. A soft brush can get more stubborn dust.