What do i do when my playstation 2 doesnt finish reading discs

Try cleaning the lens, if its a slim it should be very accessible, Use a qtip and alcohol lightly clean the lens & then try if its still doing it, check the disc for scratches and finger prints,

If the disc is dirty try bringing it to the sink in the kitchen run it under warm water, use a tiny amount of dish soap on the disc and rub it in with a circular motion, Then rinse in the warm water & dry with tissue paper for your nose or a little toilet paper, pat it dry don't rub it.

Put it back in the system and see if it works, if not then you may need a new laser which is about 20 bucks on ebay