…even if you have a modem/wi-fi card installed. You have to connect to the internet, or you have no internet access.
That is not necessarily true. If the computer has a WiFi card installed it is fairly simple to connect to any open networks in the close vicinity.
However, most older computers do not come with WiFi cards. Laptops, notebooks and tablets do. So if you get a desktop computer make sure it does not have a WiFi card.
Please note: even if the computer does not have WiFi, anyone (spouse, children) can buy a USB Wireless WiFi Adapter for as little as $5 and can connect to open networks in your area.
The best bet is to install a program that will block any Internet access.
SiDi™