127.0.0.1 is the loopback address - i.e. itself.
What that tells you is that the PC can ping itself - that means that the IP stack is loaded and functioning correctly.
The fact that you are seeing TX / RX traffic on the network simply shows that the PC is exchanging packets with the router - probably DHCP requests.
From a command prompt (Run, cmd) type ipconfig /all, then copy the result here - it will show what the IP configuration for the PC actually is.
You should also view the TCP/IP properties for the network adapter - Control Panel, network connections, d-click the relevant adapter and go into properties, scroll down to the bottom of the list - I would imagine that both should be set to automatic.
Have you any way of checking that the broadband connection is working? e.g. by plugging a PC directly into the BB modem?
The next thing to look at is the configuration of the Sagem modem - is it actually configured correctly for the ADSL connection? There are various settings that need to be correct for it to connect to the internet, quite apart from its functions as a WAP / DHCP server / Switch for your local LAN.
BTW, I am assuming it's a wireless connection as you refer to it being "connected at 2.3mbps" - am I correct in this assumption?