'classic movie' about a silent movie actress with a terrible voice after talking moviesYou're looking for "Singin' in the Rain". The character is Lina Lamont and is played by the amazing, wonderful, beautiful, and wildly underrated Jean Hagen. And she was robbed of the Oscar when that psychobitch Gloria Grahame won instead.
Image stolen from Film Experience Blog, which you should all be reading right now. So get your hands out of your pants and go read it. Damn, do I have to tell you everything?