A computer is not a standalone piece of equipment. A complete computing environment always includes a connection to the Internet. The most powerful thing about your computer is the ability to communicate or share information with other computers.
In the event of an emergency when the utility wires are down, the connection to the Internet may be disrupted. There is an alternative if there is a utility emergency.
Most cell phone services provide Internet access through your cell phone.
Cell phone service competition keeps the price very reasonable. If your cell phone provider offers a data service, it is relatively easy to tether your cell phone to the computer. It is usually just a few settings and a USB cable to get your computer connected to the Internet. You also may be able to obtain a special adapter that allows an easy wireless connection to the Internet. If you are used to a cable or fiber Internet connection, the connection speed might not seem to be the best but a slow connection is better than NO connection. Average speeds are 2-3 times faster than dial up.
Currently cities are being wired for public WiFi. Can you imagine just turning on your computer and being allowed to connect to the Internet for free? If the city has this type of service, you might have a convenient alternative to a monthly Internet access bill.
Another option is satellite Internet service. It is available almost everywhere but it is a bit more expensive than cable or fiber. Extreme weather can affect reliable satellite service but it is usually pretty reliable.
If you need just a quick email check, you may be able to use a public hotspot. Most libraries, hotels, and coffee shops offer free WiFi access.
Just bring your computer and connect but make sure that your computer is configured for a public access environment. You should have sharing disabled while you are on a public hot spot.
"I ONLY OPEN MAIL FROM PEOPLE THAT I KNOW"
A lot of people have a false sense of security. It is VERY easy to spoof an email address. You might think that you are opening an email from your friend but it could be from an impostor.
There is a new tactic in the malware war. Bad guys will hack into large organizations and create email addresses. You might receive an email from a bank that looks real. The mail did originate from the bank but it is from a hacked email account.
You have to be extra vigilant. It is not enough to trust your virus scanner or other protection software.
You have to be the final defense in any attacks on your computer.