Unless the first attack can destroy the whole country, then that's not going to happen. Ever. There's no single place where all electricity are stored and as for the Internet, you have to destroy all the cables or towers first before you can ever destroy it fully. So, let's say that a countryX have bombed countryY. Then countryY will be alarmed and the defense will all be set. The chance of countryX to destroy all these infrastructures are already gone. So like I said, electricity and the Internet will not be taken away just because it's the enemies priority for their first attack.
There's different plant or storage of electricity for different cities. There's no central one. For the Internet as well, there's tons of ISP tower all over the country.