I normally don't use tests to see if a new laptop is working.
First I do a boot test which is simply putting in the battery in the laptop if it not sealed and the plugging it in and switching it on. I see how long it takes for the laptop to take me to the setup screen. Then after it has got there I check the general performance by moving the mouse left and right on the trackpad to make sure it is working. This is of course after it has installed a lot of win updates.
Second I open up some default programs to make sure that the hdd is working.
Third I open up the default browser and see how well a youtube video plays. This should test the screen and the speakers. Also you can plug in headphones to see if the audio jack is working...