The symbiote should be a cure for cancer that the Parkers and Brocks were developing. Something comissioned by Norman Osborn, in the interest of saving his failing health.
Eddie Brock is working as a journalist overseas where the US is engaged in a country that unleashed chemical weaponry. Eddie sees that some of the weaponry was provided by OsCorp, and that the weapons are being delivered to thugs working for a crime boss based in New York (either Black Tarantula, Silver Mane, or whoever you like). The thugs are in turn selling them to both sides of the conflict. The US is aware, but hasn't intervened because it would be against their interests. They're too busy going after the head-honcho, at the cost of civilian lives. Eddie returns to the states with this evidence, and works with Peter to get into OsCorp.
Eddie gathers evidence condemning OsCorp. Meanwhile Peter, in the black suite, is fighting a city-wide gangland war against the Sinister Six: super-powered gang lords trying to carve out their place in the underworld. Peter is forced to strike a deal with one of the Six in order to stand a chance against the other five. Eddie sees Spider-Man meeting with this member of the S6 and feels as if his crusade has been worthless.
Peter is forced to shed the black suite, which promptly seeks out Eddie Brock (recognizing his DNA or something like that) and merges with him. The suite attacks his central nervous system, and tempts him with the power to avenge New York's smoldering corpse (in the aftermath of the S6 war). Thus Venom commits several violent, brutal murders related to the people he percieves as having a hand in the S6/overseas attacks.
Peter is recovering from the black suite; it provided him a temporary burst of strength/power, and left him drained and weak afterward. Thus a mentally and physically exhausted Spider-Man must battle Venom, a zealot unable to come to terms with the fact that the world doesn't work on a black and white scale of morality.
10 Year Cheesehead