PC ethernet cabled to EX6100 cannot access internet

I'm trying to use the EX6100 (FW: V1.0.2.24_1.1.134) as a wireless-to-Ethernet converter (much like the WNCE 2001, which works like a charm, but is no longer available). The EX6100 reliably connects to my home network, and I then have an Ethernet cable running from it to a wired-only (Linux) PC.

This PC can access the EX6100, my router (ASUS RT-N66U), and ping everything else on my home network. Conversely, my phone and primary home PC can access the wired-PC with no problem. In other words, everything on my home network can talk to everything else on my home network.

However, the PC that's Ethernet-cabled to the EX6100 cannot get out to the Internet. There have been multiple reboots, examination of options on the EX6100 and the router, and much searching (here and elsewhere) all to no avail.

When I connect my phone to the EX6100's WiFi, *it* has no trouble going through it to the Router to the Internet, it is only the wired connection that is being blocked from accessing the internet. (I suspect that this is a design/configuration issue, as I've seen the exact same behavior with another manufacturer's extender, i.e. it is highly unlikely that this is a hardware problem.)

I would welcome an understanding of what's happening and how to fix it--if that's doable.