Hold on, I think I missed something here... So you have an Ethernet Connection going from your Router which I assume is provided by your ISP and then you connected a Netgear GS108 Switch to it to connect multiple devices correct?
Is the Netgear one of their "Smart Switches" that you can log in to and see setting and statistics? If so check and see if the switch is seeing any errors. If not you can you log in to your router and see if there are any errors on it? Check each individual port if you can.
Also please clarify what you are talking about with the DVR Freezing up, what does that have to do with your Network Connection. The DVR is connected via Coax right? The network connection shouldn't have anything to do with unless you are talking about getting something like Netflix or Hulu from the Internet and recording it and that could just be a problem with your internet connection being slow or unreliable.
If you have the Netgear Switch you do not need another one, I though you were asking how to split the connection to connect two devices. I have two different Netgear GS108T Switches which are managed and they are AWESOME and I have no problems with them whatsoever.
The switch itself should not be causing any issues unless it is defective (which is certainly possible) OR the cable going to the Router has some issues. My suggestion would be to try running a new cable to the router just on the floor for testing purposes and see if you still have an issue. Can you connect a computer to it and see if you have any issues with the computer and if you do connect the computer to the router directly and see if you have the same issues. Again a Netgear Switch should not be causing any issues unless it is defective or configured wrong.