The first thing I would suggest checking is...all connections.
If you have a separate video card (it's not onboard video), then I suggest removing the video card and reseating it. If it's onboard video, then I would (because I have spare components lying around my apartment) try a video card in lieu of the onboard. In such cases, I have to make sure that I have the appropriate video card type that matches up with my motherboard.
The only way that I approach troubleshooting a lack of video on a system...is to try to assure myself that other likely suspects (power supply, RAM, hard drive) can be moved to another system and actually work there.
When I'm sure that the above components/functions are working properly...and I still have a problem...I move on to the hard stuff (CPU, motherboard) as suspects. My experience-level doesn't allow me to do much with these, so I just take the troubled system to a local computer shop (I trust) and ask them to check it out for me.