Troubleshooting the ps3 wireless network connection, including error 80130128

My father got a ps3 for Christmas, but ran into some problems getting it on his wireless network. The first one was "connection error 80130128" after configuring it to use DHCP. I couldn't google anything useful about this; just a few other hapless victims asking if anyone had any ideas. Fortunately Dad had his laptop there too and noticed Windows complaining that two machines on the network were both using the same IP. So, over the phone, I walked him through setting up the ps3 with a static address:

1. on his laptop, run -> cmd
2. ipconfig
3. Read the "gateway" ip. Put that into his browser to go to his router's admin page
4. Find the DHCP settings for his router to see what range of IPs it hands out; pick one outside that range
5. Set up the ps3 with that IP, the router IP as primary dns, and an opendns server as secondary

This made the connection test happy. But when he tried to go to the playstation store, it gave a DNS error. If he repeated the connection test again, it failed too. "Well," I told him, "It's supposed to try both DNS servers. But we can try setting the primary DNS server to opendns as well." Once he did that, everything worked.