OK. The problem solved. The Internet is back. Yay!!
FYI, the problem was not the modem itself. It was more like the balance of the speed of downloading and uploading, as far as I can understand. The system I'm using is called ADSL, one of the broadband services. And it seems like that when the above mentioned balance is no good, the connection becomes unstable or dead. That was the answer I got from the net search.
Now the question is why the balance which had been OK for years becomes "no good" one day, all of sudden, even though the setting is absolutely untouched. But looks like it is difficult to nail down the specific cause(s) of the problem, and ISPs -- at least here in Japan -- do not really help you with the investigation. What they do instead seems to be adjusting the speed balance at their end. I heard that it does regain the connection, but slows down your Internet (of course-- why would they make it faster for free?).
Well, in my case, the connection seems to be OK now and the speed is just a little bit slower but not too terrible, so I'm happy. The good thing is that the problem was solved real quick with no charge, and I didn't have to bring my modem to the store or clean up my apartment to have people come into my room to fix some lines and cables. Phew!
Anyway, now that my Internet connection is fine, I wanted to let you know that I soaked some dried fruit again for Christmas fruitcake. I might go for a light fruitcake this year, with less or no molasses added, and try more simple and plain decoration... like this. No icing at all. Or I might go for a real heavy, classic pecan-nuts-and-cherries topping. I don't know. You'll see. ;) I've been looking for ideas through google image search. Isn't it great? The Internet rocks! I can't live without it -- definitely.