generally you can't run more than 3 monitors off one card period. Only AMD cards allow this and only with display port monitors (or active display port adapters). So which GPU do you have? If you have both onboard and discrete graphics it may be possible to run them both at the same time to drive 3 monitors.
FYI your harddrive is the thing inside with the data on it(and def doesn't have HDMI), the thing with the HDMI is your GPU ( or motherboard if you have onboard graphics) , and the computer would be the whole box.