This phase II trial is studying how well giving bortezomib together with paclitaxel and carboplatin works in treating patients with metastatic melanoma. Bortezomib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as paclitaxel and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Bortezomib may help paclitaxel and carboplatin kill more tumor cells by making tumor cells more sensitive to these drugs