I am looking to transfer to another job in Washington State. My visa is valid for another 2 years. What is the process and the money involved to do so? Do I have the employer submit a new LCA, or a LCA and an I-129? Do all those fees have to be paid again? I can't get a straight answer without paying for it first.

You have to pay all the fees again in order to transfer your existing H1 to another company