Sorry man, your idea has been taken already... they are called uninterruptible power supplies (UPS). They can seamlessly keep your computer and other similar electronics online with a battery backup until power is restored. For longer outages, most folks use an outdoor AC generator to power critical components (fridge, freezer, heating, maybe computer/modem).
Also, your DC power outlets idea would not work logistically. Your modem and computer do indeed have power supply cords that convert 120 VAC into some DC voltage. So, in order to use your special DC outlets during an emergency, you would have to unplug the devices from the normal outlets, attach a special DC-DC cord, and then plug the device into the emergency DC outlets. So, this would be quite the headache and would also mean downtime while you switch over; by comparison a UPS would have no downtime. Also you have to figure in the additional complexity of installing emergency DC outlets in a home (more confusion for electricians and homeowners).
Finally, a gas-powered generator in the basement isn't the best idea since internal combustion engines give off carbon monoxide. People have died from using products such as gas-powered pressure washers in enclosed areas. In fact, a fairly common way to commit suicide is to leave your car engine idle in an enclosed garage.
So... I propose sticking with the status quo here. AC outlets for all, and UPS devices for those that need emergency backup power for their computers (in your case to keep your phone service as well).
edit: Oops, you did mention that you know that battery backups exist already. Still, the points that I and others have made still stand.