OS X V10.7 Lion :: Ethernet Internet Connection Fails But Not WiFi?

I am on a Mac Mini connected to the Net via a FON wireless router and Ethernet directly to my broadband modem. I have had problems with both the modem and an Airport Extreme, which eventually died, but I am back up again with the modem via the FON router.The odd thing is that I can't get Ethernet to work over a direct connection to the modem. Diagnostics tells me that the ISP and Internet fails. I can connect to the modem over Ethernet, however, change its settings etc. in my browser. There are solutions mentioned here involving changing the etc/authorization file, but wouldn't that also affect the WiFi if that was the problem? 

In short, Ethernet connection to modem works. WiFi connection to FON router and then to the ISP and Internet works. But the Ethernet configuration does't go that last bit, it only works locally. Using that route, I can't connect to the outside world. I have restarted the modem, the computer etc., but that should not be the problem as both works over WiFi, using the same settings for the modem. How do I best troubleshoot this? I am getting an AirPort Express, perhaps it will work better with the modem that the computer itself, but I doubt it.

Info:
Mac mini, Mac OS X (10.7.4), 2.3 GHz Intel Core i5