Hello everyone, I am using this post as a method of sharing how I solved my own problem and to hopefully help others as I was unable to find any other information regarding this topic. I will mark my answer to this question in the answers section.
The Problem: Netgear Gigabit Network Switch (GS116NA) shuts down entire network when plugged into a Comcast supplied modem/router combo.
In previous years, my network was only 10/100 because my ISP only supplied me with about 25/5 internet speeds. And I had no other devices on my network that I needed to communicate to other than to move small files around. These files would not be bottlenecked by this connection. I used Netgear 10/100 switches and cat5e cable (cat5 in some places) to connect my entire network which at the time was mostly wireless. Now, I have upgraded and my ISP now supplies me with 250/15 internet speeds and obviously, I was unable to get the full potential of my network using the connections prior. So I did what anyone would do and I upgraded all the cabling, AP's ad switches to gigabit. I did already have one Netgear switch that was gigabit, but it was at the end of a 150ft cat5e run and strangely would not work at all unless there was another Netgear switch (a 10/100 switch) supplying it. Using my standard modem would not work, it would only work when two switches were connected to each other.
Overall, I was really stumped here and have yet to find the solution to my issue. It seems as though I may need to just replace the switch.