 This phase II trial studies how well androgen deprivation therapy and vorinostat followed by radical prostatectomy works in treating patients with prostate cancer that has not spread to other parts of the body. Androgens can cause the growth of prostate cancer cells. Antihormone therapy, such as bicalutamide, goserelin acetate, and leuprolide acetate, may lessen the amount of androgens made by the body. Vorinostat may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving androgen deprivation therapy and vorinostat before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed. 