Have you doubled checked the cable connections, do not try to remove and reinstall while it is running, just make sure they are secure. If this is a new computer and you put it together, this is more than likely the problem. Is there a trouble shooting manual in the box?
If it was shipped to you, a connection might have come loose inside. If you go inside, make sure you unplug the power cord and ground yourself before touching any of the components.
You monitor is on, right? Does it have a signal light or just an amber or some other no signal indication?
Do you hear any beeps during startup?
I would guess shutting it down will not have any ill effects, but do you have a choice?