Your screen could be black for a few reasons.
1. Your computer could be hibernating rather than off. Try moving your mouse, hitting the space bar, pressing the On button a few times, or turn it off, unplug it, wait two minutes, plug it back in and turn it back on.
2. Your monitor could be off, or one of the knobs or buttons on it might have been moved and needs to be moved the other way to show the picture.
3. You could have a virus that is affecting your screen and/or your bootup hardware or software.
Even with good anti-virus software, viruses and malware do sometimes get in - that's why you run periodic scans as well as just letting it run in the background all the time.
You may or may not have a virus. Scam pop-up windows aren't always viruses. The pop-up you got saying you don't have genuine Windows is very likely a scam. You can check right on the Microsoft website whether it's genuine or not, here:
http://www.microsoft.com/genuine/val...displaylang=en
But get your monitor working first, and also run a full virus scan and remove any viruses.