Do areas with depleted resources count for Jim Raynor's victory condition?
Yes, depleted areas do count. From the FAQ:


  Q: If an area has been fully depleted of resources, does it still
  count towards players’ special victory conditions?
  
  A: Yes. For
  example, Jim Raynor needs to control six areas containing gas and/or
  minerals; this includes any area that has a printed gas or mineral
  icon on it.