Now my previous connection required the modem to be configured to this address. So the problem lay in some remnant of my previous configuration which had creeped into IE. I deleted my previous connection from "Network Connections". Yet the problem persisted. IE was still trying to connect to "192.168.1.2". Now I had to look up a setting which was not changed even after deleting my previous connection. After some search, I found that my LAN settings were set to use "192.168.1.2" as proxy. I unchecked that option and tried to connect again. The problem was solved now.
Yahoo messenger used IE internally. So it was also not working on my system. But now I can happily use Yahoo Messenger again.