I think, if I'm understanding this correctly, that everything works fine when you connect to the Asus device, but the problem is when you bypass the Asus and go directly to the LAN ports on the Westell, we can safely say that the issue is not with the computer itself or the software products installed but more likely an issue between the Gigabit NIC and the Westell.
Some gig nics just won't autonegotiate properly with some routers, this may be the case with the Westell.
You can try setting the speed and duplex on the NIC manually to 100 half or more preferably 100 full just as an experiment to see if we're on the right track. If you need help with that post back and we'll go through the steps with you. Make sure you experiment with...