Basically, if you put in a new cartridge and it leaks, then it is bad and you need another one.
But try this....remove the handle, and just with the blunt end of a screwdriver, push the cartridge all the way in. If the drip stops, it tells you there is a missing washer, or some other little thing, wrong with the handle attachment which stops it from going all the way off.
But otherwise, just get another new cart. Make sure it is genuine Moen brand.