Laptop screen sometimes doesn't work. Is it the LCD cable?

"I am guessing this is probably a ribbon cable? If not please put more detail in.

The cable(s) would likely be stressed by the bad hinge, but that doesn't mean the LCD itself is not bad. If you can try and spot-check to see if certain positions work better than others (if you're brave enough to turn it on with the case open like that) that could tell you if the cable is bad. I would likely just try and reseat the cable or cables and put it back together, hoping for the best.

Also, of course the inverter could be a problem as well. Just as in a desktop, a problem could be the power supply, motherboard, sound card, memory, graphics card, etc. Everything and anything would likely need to be checked. Unfortunately, without another of the exact same model of laptop its hard to troubleshoot."