The fatal errors you were receiving are likely related to your issue. And I can tell you that your problem has nothing to do with a virus if your computer does not display a video signal.
First, check the obvious - This may be a coincidence. For example, you were having blue screens before, but now your monitor cable has become disconnected so you have a blank screen. So naturally your first assumption might be a virus or system failure.
After you check the obvious, we know that this is almost certainly a hardware problem. Judging by your description, the great probable causes include CPU (overheating, defective), video card (defective, improperly seated), memory (defective, improperly seated), power supply (defective) and board (defective, shorted).
Out of those, I'd check the video card first. For example, something I might try is turning the computer off, pop it open, pull the video card out and reseat it inside the slot. Turn it back on and see if it works. If that doesn't work, then I might try to get ahold of another video card or remove your own video card and try it in someone else's system to cross check it. You may also have integrated graphics, so you can't remove the video in these systems.
There's a lot of stuff to troubleshooting this kind of error. If you aren't skilled enough with handling these types of problems, you might be better off getting a computer service professional or knowledgable friend to help you out. Otherwise, you may not have the equipment etc.. necessary to effectively troubleshoot.
Since there are no POST beeps, we don't have much to go on. There's so many reasons this kind of thing can happen.