No, your auto insurance would not cover a mechanical breakdown such as a blown engine that was not caused by an accident or other incident that would be covered under the terms of your policy.

You can check with your state's consumer protection agency to see what your state's lemon laws are regarding this type of situation. Normally they only cover new cars though. If your car was purchased with a warranty or mechanical breakdown insurance policy then you would be able to put a claim through this they of policy.

If you bought the car used and in "as is" condition then normally you do not have any recourse against either the person you bought the car through or your insurance company.

Coverage for specific parts of your vehicle, such as the engine or transmission, to be repaired or replaced is usually done with by means of a warranty. Warranties can be purchased at dealerships, financial institutes or online.

Some financial entities also offer mechanical breakdown insurance which would cover mechanical issues with your vehicle. If you believe you purchased this when you got financing for the car then contact your lien holder to get information on the breakdown insurance provider through which you could make a claim.