Hey Houlihas,
I hope you are having a great day (well...besides the connection issues).
After taking a look at your screenshot, it *does* look like the issue is most likely with the connection between your computer and hop #1 (which is most likely your modem). Anytime you see packet loss that carries through to the final target, you can follow the packet loss up to the earliest hop the the packet loss starts at and the issue is *usually* between the hop before that hop, and that hop.
In your case, I think you would definitely be starting in a great place by replacing all the patch cables and re-crimping the uplinks. After doing that, trace for another 12 hours and see if there is a difference in your connection going down and the amount of disconnects that happens.
We have a great guide for troubleshooting your network using PingPlotter here:
http://www.pingplotter.com/netnirvana/I hope this helps. If you need any other help with this or anything else, feel free to email us at any time.
Cheers!
-Phillip