> connecting my computer directly to my modem (bypassing my router) seems to make my connection
> return back to its original state.
I take it that you're using some kind of ADSL over telco lines then?
Does making a normal phone call have the same effect as using a dial-up modem?
Does your cable modem have any kind of setup page?
Open a cmd.exe console, type 'ipconfig'
Then in your browser try connecting to http://192.168.1.1 (or whatever your Default Gateway address happens to be).
For example, I can get a page like this
Pay close attention to things like line rate, noise margins and error rates. Get to know what a "good" page looks like and compare with a "bad" page when things get worse.
Also, do you have a splitter/filter block which splits your telco line into phone and ADSL. Have you replaced that?