A venture capitalist with political ties sought to help Silicon Valley entrepreneur Gurbaksh Chahal “do whatever it takes” to resolve a domestic-violence case so that a planned initial public offering could move forward, according to documents reviewed by The Wall Street Journal.

Mr. Chahal, founder and then-CEO of digital-ad company RadiumOne, was arrested and charged in August 2013 with 45 felony counts after San Francisco prosecutors alleged he struck his girlfriend more than 100 times over a 30-minute period in his apartment....