Just to explain, the problem is that when there is a blackout, cellphone towers can go down because of the blackout itself, and even if they don't, they can get overloaded because suddenly everyone in your neighborhood is using them instead of wifi. This can lead to an inability to connect to the internet even if you have a laptop that's running on battery. However, the adsl / dsl gets its power from the landline phone company which is far away and always has backup generators and so it almost never goes down. But if you have no power, your modem won't work, so all you can do is make phone calls, but no internet.
So what would be helpful is a modem that can be powered through usb alone, and is able to provide an internet connection to the laptop by connecting to the adsl / dsl phone landline directly. What I imagine is something that looks like a usb stick that you just plug into your laptop, and plug the phone landline on the other end. Or perhaps a larger sized modem that has one usb cable coming out to connect to the laptop, and has a receiver port for the phone landline.