I would definitely take a look at the DHCP settings... if only to rule it out.
When you run into one of these "odd" problems, I find that it's best to try and isolate the trouble to a specific area. In other words, spend some time figuring out what is not causing the problem.
I like to draw a little diagram showing the flow (logical or physical or both) from the machine having a problem to whatever server/network/etc it should get to. I include every device that it touches. Then, it is just a matter of testing each device until I hit the one that is not working.
You've already been doing this (replacing the cable with known good, for example). My point is that I like to start at the computer (check settings) then work my way out until I hit the problem... checking everything along the way.
Back when I did tech support, I learned to verify, verify, verify. There is nothing worse than spending hours troubleshooting only to realize that the problem is caused by a setting you assumed was set correctly (port number, whatever).
Specifically in this case...
- Verify that the computers are using DHCP and do not have static address/mask/gateway
- Try pinging the FS116, Firebox, and Westell modem from a problem computer
- Disconnect both problem computers from the switch and move a working computer's cable to one of their ports (ipconfig /release; move cable; ipconfig /renew... just to be sure). If the working computer still works, then you can pretty much rule out the physical layer
- Go through server settings and make sure they are correct (DHCP, router settings/filters)