In case anyone gets the following connection error: 80710102 when trying to get online with their ps3 here is my experience and the way to fix it.
Until today, I never had any issues getting online, I have a wired connection into a router, acting as DHCP server, then into a cable modem. Today, though, I could not get online, I was connected to my router, but not to the internet. I kept on getting the above DNS error code. After searching around here, I couldn't find a solution, so I began to look at the problem more closely. Your ISP provider typically gives its customers several DNS IP's and these are stored in your router in the setup menus, usually on the very first page. The ps3 automatically gets the top two DNS IP's and stores them in your network config menus. If, by chance, your 1st DNS IP goes dark and is not recognized by your internet provider, then typically, the client (usually a pc) attached to the router uses the next one down the list, so no problem. BUT, with the sony ps3, there is a problem. The ps3 does not go to the second stored DNS IP. The solution to this problem, if it happens to any of you, is to manually enter your DNS IP's, but reverse their order of importance. Once I did this, I had no problems and internet activity returned as usual. I did a search on Sony's tech support forums and found countless people having similar issues. Hopefully, Sony will fix this annoyance in a firmware upgrade, in order to utilize the second DNS entry but who knows?