So you have an ADSL modem and
a Linksys router, right? Which modem and what model Linksys?
Modems die. When they do they start the process much like you've described. Just had one die on me last week... luckily I had a spare, but, they do, especially the really cheap ones your ISP hands out.
If it's the Linksys router, you could try upgrading the firmware. If it's a bad NIC driver
, you could search out an earlier version. If it's the modem, you'll have to either buy one, or get your ISP to send you one.
Hit the Windows key and type in cmd, press enter. Type (without quotes) "ping 127.0.0.1". If the loopback test is successful, then the problem isn't your NIC. In that same command prompt, enter in (without quotes) "ipconfig /all" and hit enter. Look for your Default Gateway and write the number down. Ping the default gateway. For example, "ping 192.168.0.1". If this is successful, then it isn't your router; thus, your modem is on it's way to an early grave.