if you get a black screen, it is mostly a graphical problem, mainly a screen size problem. delete your settings file located at C:\Program Files (x86)\Steam\SteamApps\common\call of duty black ops\players and delete either the config_mp.cfg or the config.cfg file, depending on which gamemode the problem occurs.
if you have a new graphics card, the problem might be there. delete your graphics control program and install the latest drivers from their website. i hope you got an nvidia cause the games are mainly tested and playd on those.