Is there a state of matter in which the molecules are not moving at all? What is this phenomenon known as?

No

Explanation:

There is no possible physical way for there to be an object without the molecules moving. There is a temperature called absolute zero, * however, there will always be some form of heat to touch everything, so nothing will ever be "frozen solid."

(*) By international agreement, absolute zero is defined as precisely; 0 K on the Kelvin scale, which is a thermodynamic (absolute) temperature scale; and - 273.15 degrees Celsius on the Celsius scale.