In reply to:
do modems/routers have different characteristics which can make this possible?
A useful summary is
here
The major difference between a router and a modem is that you use completely different technologies to communicate between the computer and the device which connects to the ADSL link.
Most ADSL modems use USB which, I have seen it suggested, will be a slow point in your link. A router connects using Ethernet (or some other network setup) which will normally be far faster than anything else in line with it.
Other problems arise because the modem is essentially connected to a single computer. If you wish to use a network, that computer must also run network sharing (Windows Internet Sharing or some third party proxy server) so that other computers can use the link. I have done this and, believe me, it is an experience I will never willingly repeat.
Even if you only have one machine, a router has major advantages. It is completely separate from the computer. Therefore it handles the connection. With a modem, most of the work is done by the computer, using, with Windows Dial Up Networking (DUN up to Win98) or Remote Access Service (RAS - NT/XP). You can leave it on all the time or, if you want to turn it on or off, all that is needed is the mains switch (which could even be on a timer). This has two advantages:
It doesn't consume any resources on a computer.
Because it is a separate device, it is an ideal firewall. No malware, should it infect your coputer, can turn it off. Many viruses are capable of disabling at least the commonest software firewalls.
I doubt whether it is worth trying to find out if your problem is due to one of the disadvantages I have suggested here, or something else. You have shown that the router works and the modem doesn't, why not just dump the modem and use the router instead?
I would make the same recommendation, even if you were not experiencing problems with the modem.
John Underwood