Hi Josh,
Sorry about all the issues you are having. Hopefully, we can work together to help you resolve your issues.
First, I am also a Comcast customer, and I have Internet, Cable TV, and landline phone service with them. My "device" I have for the internet is also needed for my phone service, and it is a Touchstone TM722 Telephony Modem. I also have a Netgear router. Once in a while, there are issues with the internet and Comcast. One thing that works in a number of instances is to follow Comcast's procedure about shutting down the modem and router, waiting the suggested amount of time, and then turning those pieces back on (in the correct order). You might want to try that.
As for backups, I am not certain whether Time Machine backs up OS/System files, folders, etc. (I don't believe it does). I myself use SuperDuper! to make a bootable backup/clone of my system. While I do this manually (I can set it up to do "automatic"/sequential backups, similar to Time Machine), for my needs, it works fine. The important things are 1) a bootable backup is made, and thus can do an instant recovery, and 2) all OS/system files, folders, etc. are backed. I just posted a thread of some issues I had with my Mac Mini over the weekend, and in it, I described how beneficial my SuperDuper! backup was.
If you are posting here via your iMac, not sure how "stable" the OS pieces are. You might want to consider doing some kind of backup, mainly for the non-system files and folders. You would then restart your iMac from the Snow Leopard DVD (I assume you have it), use Disk Utility there to Erase, Format, and Partition the internal drive, then do a fresh, new installation of Snow Leopard. I of course do not know what version of Snow Leopard you have via the DVD, but if it's anything less than 10.6.8, you would then need to download and install the OS 10.6.8 Combo Updater. You can get that from here:
https://support.apple.com/kb/DL1399?locale=en_US
Once that is done, and you reboot your iMac, you can use Migration Assistant to retrieve all your non-system files, folders, etc. from the backup. I have recently gone through something similar, but I am using Yosemite (OS 10.10), and just like you, I need to upgrade to OS 10.10.4 via its Combo Update (I have it already downloaded). As for using Migration Assistant, given that I use SuperDuper! for my backups, I know how to do it with such backups. But, I do not know how to do it from a Time Machine backup. I suspect, though, that it is a simple process.
By the way, what brand of mouse are you using?