Yes they could have a restriction on routers/APs but you should be connecting to the WAN port. If you connect to an LAN port their router needs a static address for the AP that you are trying to configure and they are not going to do that.
Start out by resetting your router to default settings by depressing the reset button on the back (probably in a small hole). Attach a computer to the router LAN port to configure. Once it is working properly use wireless not until then.
You might have to clone a computer MAC into the router and that process should be detailed in your Buffalo manual.
To login to your router are you using the default ID and password also root and ? You should be able to set everything up from scratch.
I would try resetting it again. This time disconnect the Internet and LAN cables then press and hold the reset for 30 seconds allow it to boot up for 2 minutes then unplug it. Wait a moment then plug it back in give it 2 minutes to fully boot then attach an LAN cable for the computer to configure it and try getting to the configuration page.
By default it may not have any wireless security but probably does have DHCP enabled.
All that I suggested was a way to get into the router to change the settings and it seems like that worked. So you now can connect with the wired connection and your phone. Did you set the new security password in the other devices?
As far as the quality of your wireless you are probably surrounded by wireless networks that will interfere. Download and run the free INSSIDER wireless analyzer on a computer that has a wireless adapter to see the surrounding network by channel so you can try to avoid the stronger signals.
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