It took 3 hours to get this working. I'm not sure who to blame: Belkin, for a potentially crappy DHCP server, or Roku, for a potentially crappy DHCP client. Either way, switching over to my Linksys access point for DHCP fixed the problem.
Of course, I added the Belkin in the first place because the Linksys didn't play at all well with a Broadcom wireless chipset I had in one of my laptops.
I blame Belkin. I've never been impressed with any of their products. I wouldn't buy anything fancier than a USB cable from them.
Blame them all. I've worked with parts from most major vendors—the only thing that's good about them is that they suck in different ways.