I guess my first thought would be to try another computer and see if you still get the same issue. If you do then you know the issue is not being caused by your system. At that point you call your ISP back up and tell them that you have the same issue across multiple machines.
At this point(unless you own your own cable modem) it is in your ISP's court. ISPs are very notorious for passing the blame onto your computer just because it's a lot easier than trying to do the work to fix the issue themselves.