Is everything on the computer slow or just your browser/internet. A good place to start would be to run some speed tests and see how fast your connection is on each computer. If you're getting 80% or more of what your ISP is suppose to be giving you you should be OK. You can also see the difference between machines. DSLreports.com also has several speed tests and a tweak test. There is also a link to a program called DR TCP/IP that you can use to adjust some of the settings that the tweak test may recommend.
You can try swapping cables to see if it helps. I doubt it will but it's pretty simple to try. Also get rid of programs running in the system tray that you don't really need running all the time. WinRAR and such. That should help speed up your computer startup and improve your speed of everything. You can look in your startup folder and see if there are any programs the run at startup thet you really don't need all the time. Also you can run msconfig from the run.. dialog and set up selective startup to stop some of these.
You should also check your browser/tools/manage add-ons and disable some of those if you have alot of those. It is pretty to reenable them if you want to. You can reenable startup programs and add-ons one by one to see if maybe one of them is causing the drag on your system or if that is even the cause of the problem.
If you've got plenty of disk space on each partition and are running the defrag regularly that is very positive. One final thing is that it might be the NIC card (network interface) if it's dropping packets then that would explain the modem and router activity you describe. The DSLreports tweak test should tell you if you have a problem there. The fix could be adjusting the RWIN or MTU setting which you can easily do through DrTCP/IP. If the card is going bad then you would have to replace it or put in another one if your existing one is built into the motherboard.