First rule is to give us the brand, model, and age of the laptop. We don't have enough information to help you.
Is it under warranty?
Any attempt to open the case by buggering up a screw voids most warranties.
Laptops are held together with a few (6 to 12) screws and some plastic snaps. You need to first remove the hard drive, memory modules, battery and optical drive to get to the parts that matter for a disassembly.
Most laptop screws are held in by blue or red retainer compound, so you need to know how to use a screwdriver. The first step is knowing which screwdriver. The second is knowing how to use it. Since you have apparently already disabled the system by buggering up the screws, you need to get some knowledgable help.
But as you go, you will need to figger out where the case clips and snaps are located, or you will break critical components that hold everything together.
From a tech standpoint, you have already shown you need help by buggering up the screw... either your screw drivers are poor quality or incorrect sizes.
You can easily get to the point where it will cost you real money to deal with getting this computer back to original condition.
Most laptop schematics are available on line, via a Google search, or the website of the manufacturer... remembering that you are voiding the warranty and upping repair costs on whatever you do.