A Dell Vostro 3520 has a motherboard and IO board. This computer has the motherboard separate from the IO board, and the IO board connects to the power button. This particular Vostro 3520 that I was working on had a corroded connector. The corroded connector connected the IO board to the motherboard, and this connector was preventing this computer from powering on. The power button is connected to this IO board and a ribbon cable connects the IO board to the motherboard.
A simple cleaning of the connector and ribbon cable allowed the computer to power on when pressing down the power button.