Fix: From doing some research, it seems that the Nintendo Entertainment System just needs a good cleaning. The issue seems to be stemming from the connector pins. Here is a video of someone fixing this issue:
Current NES Value: Out of box working NES are around $60 on eBay. Since this one comes with the box, it is worth much more. The cheapest NES with a box that I found was this:
With 28 watchers, this listing is not going to be up much longer. What does this mean? It means you can charge more for it. I would say you can get around $120.