You unplug your charger and the MacBook closes right! Perhaps it works, but dies very quickly, or works until it hits 50%, then turns right. This is common, as laptop batteries rarely make it in good condition for over two years.
We stock most MacBook batteries and can often replace them with a one-day MacBook repair service that has no parts. We also do Retina MacBook Pro battery replacements; Many repair shops do not offer this repair without replacing the entire top case. Apple has designed some of its laptops in a way where the battery cannot be replaced, and replacing the top case is very expensive.