That's actually pretty close to the plot of (spoilertagging the name of the book because this is kinda the whodunnit, though it's pretty unsurprising by the time it gets there) [spoiler]Rule 34 by Charles Stross[/spoiler]. Though that's exactly the book I was thinking of when I said I'd read stories with similar premises but they still hinged on the question of computer becoming sentient.
I don't remember the exact details, but -- spoilers for the same book -- [spoiler]a complex data-gathering tool is repurposed as a spam filter, and ultimately it starts orchestrating elaborate murders of people involved in the spam supply chain, by analyzing their browser and purchasing history. Household appliance malfunctions and when they go to 3D print a replacement part, the filter changes the schematic so that the part will be faulty and cause a lethal malfunction, that sort of thing.[/spoiler]
