if you did not complete your contract, you would not be owed the $3000. You specifically state you returned unfinished cases to them so why would you be owed for work not completed?
It sounds like you need to determine the value of the work you are actually owed for and make a claim for that. You have to realize that some work you refused to complete but had started may have no value at all if some other lab cannot complete, or will not complete, what you started.

